My idea has been a colonized planet or moon with incredibly strong winds so that life is only possible in deep valleys protected from the wind. I recognize that wind is primarily driven by temperature differentials. So my question is this...on a moon that is tidally locked to its planet, would the temperature differential between when the moon is in the planet's shadow and when the "light side" is exposed to the system's sun conceivably be enough to drive super-strong winds?
The answer can be "sure," but it depends on how you build everything else about the system. Let's set up an example.
The gas giant will always act as a shadow. It doesn't matter how hot or cold it is because the moon must be outside the atmosphere (or the drag caused by orbiting through it would eventually bring it down) and an atmosphere is needed to capture convective heat. If the gas giant is creating radiant heat, the moon is baked like a potatoe left in a microwave too long.
The sun needs to be hotter than what we're used to. This way, when the moon is on the sun-side, it's cooking up a storm.
Lunar volcanism can add to this, but let's ignore it to keep the issue simpler. Lunar water would add a LOT to this, but let's ignore that, too, since it would really only make things worse and if the idea is bad enough already then it's unecessary to include in the analysis.
If you imagine how the sun hits the moon during its orbit, the moon comes out of the shadow of the gas giant and the sunlight heats a sliver of the moon's surface. that grows until the moon is half-way between night and day side of the gas giant. Now the sun is heating half the moon. 75% of the moon's surface is heated as it progresses around the sunside of the gas giant until the half-way point, then the surface heating decreases from half the moon down to a sliver again. That's a lot of lunar surface to heat, but the important part is, the planet-side face of the moon (well, a portion of it) is never heated.
Which means you have an atmospheric low-pressure zone that's always over the equator planet-side and a basic high-pressure zone that moves across about 85% of the moon's sunward surface every orbit. That sounds like a centerfuge to me.
Therefore, there are substantial thermal gradients involved that could, depending on the nature of the moon, the distance of the gas giant from the sun, the heat of the sun, and a small army of other factors, create the winds you're looking for. The winds would die down to a low point just before the moon emerges from behind the gas giant (just a little bit like the planet Crematoria from the movie The Chronicles of Riddick, but it's a useful image).
Now, having said that, please be aware that deep crevasses will provide only partial protection. That's because the howling wind above creates a low pressure zone inside the crevasse. During the orbital cycle of the moon, that pressure bounces up and down, creating winds of its own depending on the depth, length, and shape of the crevasse. They'll also be a firestorm of dust kicked up from the winds above and dumped when those winds impact the rim of the crevasse. Finally, if the crevasse is along the path of the wind, they'll be no protection at all.
Where they would be beneficial is if you built into the side of the crevasse deep down. But, there's little difference really between that and building underground anywhere else.
Do you mean life for the Human colonists is only possible in the deep valleys or that any type of life is only possible in the deep valleys?
Either the Human colonists live in closed moon base type structures with their own air, or the Human colonists breath the air of the moon, which means that they breath the oxygen in the atmosphere that is produced by native plants. Either there are some types of native plants on the surface despite the winds, or else there are native plants living in the oceans of the moon, or both. In any case if Humans breath oxygen in the air of the moon there is plant life on the moon.
A moon large enough to be habitable for humans, except for the wind speeds, is likely to orbit in the equatorial plane of the planet it orbits. It would have to be much larger than any known moon in our solar system, for example, in order to retain a significant atmosphere while being warm enough for Earth type life.
All the large moons and many smaller ones in our solar system except for Earth's moon orbit in the equatorial plane of the planet they orbit. All of the inner moons of the gas giant planets seem to have been produced from the same cloud of space dust as their planets and thus share its rotation and orbit in the equatorial plane of the planet.
The outer moons of the gas giant planets do not orbit so close and are believed to be captured asteroids and thus have more inclined orbits.
Io, the innermost large moon of Jupiter has a month and day 1.769 Earth days long. On the side of Io opposite Jupiter, the sunlight and the night each last for 0.8845 Earth days or 21.228 hours. Thus that side would heat up during daylight for longer than Earth does, and would cool off during nighttime for longer than Earth does. If Io received as much light from the Sun does, the temperature variation between night and day would be greater than on Earth.
On the inner side of Io, that always faces Jupiter, the length of daylight and nighttime would be the same as on the outer side, except that eclipses would make the period of light shorter. Jupiter would appear to be 19.5 degrees wide as seen from Io, so the eclipses should last for about 0.0958 of an Earth day or 2.299 Earth hours. Thus on the average the inner side would be a little colder than the outer side.
Callisto, the outermost large moon of Jupiter, has an orbital period and day of 16.689 Earth days. Because it is 4.465 times as far from Jupiter as Io, eclipses on the inner side of Callisto only last about 0.20 hours or 12.14 minutes, which is a much shorter percentage of the 8.3445 Earth days of daylight that the inner side of Callisto receives. But over eight days of light followed by over eight days of darkness will certainly give Callisto more time to heat up and cool down.
So a habitable moon with a Callisto-like orbit would have large temperature differences between day side and night side leading to strong winds from the day side to the night side.
Thus the land surface of the satellite will suffer extremes of heat and cold (which are necessary for super strong winds) and might not have land based native life. But the oceans should not have such extreme temperature differences and ocean plants should be able to provide oxygen for the Human settlers to breath.
So it seems to me that you shouldn't worry about the temperature differences and winds caused by eclipses, but instead about the temperature differences and winds caused by the length of the moon's daylight and darkness, which can be a number of Earth days long.
Iapetus, the outermost regular satellite of Saturn, has an orbital period 79.3215 Earth days. Thus daylight and nighttime each last 39.660 Earth days. If Iapetus received as much sunlight as Earth does, the differences between day and night temperatures would be great.
A large, habitable moon of a giant planet would, as I said above, probably orbit in the equatorial plane of the planet. And thus it would share the axial tilt of the planet. The axial tilt of planets in our solar system varies from 0.03 degrees (Mercury) to 82.23 degrees (Uranus). The plane in which the moons of Uranus orbit Uranus is almost 90 degrees and perpendicular to the plane in which Uranus orbits the Sun.
Thus during part of the Uranian year the northern hemispheres of the moons of Uranus have constant daylight and the southern hemispheres have constant darkness, and during the opposite part of the Uranian year the southern hemispheres of the Uranian moons have constant daylight and the northern hemispheres have constant darkness. Since the year of Uranus is 84 Earth years long, the periods of constant light or dark last for several Earth years. For most of the Uranian year the moons have more normal and shorter periods of darkness and light.
There have been several scientific papers discussing the parameters of hypothetical habitable moons in other solar systems, and I have referenced some of them in other answers.