Let's use Mercury as an example, we can pretend it orbits in the habitable zone of the Sun, would Mercury's magnetic field be able to protect an Earth like atmosphere? And would the lower gravity mean larger creatures? Also by Earth like atmosphere I mean similar composition, not pressure.
Not, it is not possible, for a number of reasons.
Atmospheric Escape prevents small planet from keeping an atmosphere over the long term. The difference in escape velocity means that just about every type of gas would be gone after a few million years (xenon would be an exception). The wiki article include a graph showing Mercury in particular.
A small planet cannot maintain a strong magnetic field over a long period of time. The smaller core will cool down more quickly and any dynamo effect will dissipate as the liquid iron slows and eventually stop. Mars is a good example, although larger than Mercury and having a strong magnetic field in the past is no longer protected by a magnetic field.
All liquid water will disappear from the surface on such a planet -- it would boil away under the reduced atmospheric pressure and then escape quickly into space as it is a fairly light molecule.
Without atmosphere, expect large diurnal temperature swings.
For comparison, Mercury (4789 km diameter) is really not that much larger than the Moon (3475 km) -- the moon has suffered the same fate as Mercury would, albeit somewhat faster since it is even smaller. The outcome would be identical though.
Gary’s answer is exactly right. I’ll continue with how we might make it work anyway.
Look at Ganymede, which if half the mass of Mercury and has a magnetic field! It does not need to generate a powerful field, as it can simply borrow Jupiter’s. Consider how a piece of plain iron (or a paperclip) acts like a magnet itself when it’s near a powerful magnet. Plotting the field lines and then cropping the diqgrqm to show only the secondary object, it appears to be a magnet itself! That’s because it concentrates the field lines passing near it.
So, put a gas giant in the habitable zone and make the ☿-sized body a moon of that.
Now, how about atmospheric loss? The presence of the magnetic field will prevent solar wind ablation, so you just have the slower loss from lack of gravity. Again, making it a moon helps: gas escaping can be balanced with gas infalling. In genereral the gas escaping the moon will not be escaping the primary. But you want it to form a gossamer ring and be swept up again, rather than spreading out and eventually falling onto the primary. Arrange this by having multiple moons in orbital resonance. The gas molelules will feel the “notch” too and be attracted to that same orbit. Maybe it receives gas from the farther-out moons, too!