Could space travelers save space inside their craft by trailing freeze-dried meat on a rope (space tether) behind their space pod? Presumably nothing would be able to get it out there, and it wouldn't spoil. Would this be hazardous?
It should be fine, but you won't win any cooking awards. I don't think the meat would be instantly dehydrated per se; most of the fluid in the meat would freeze solid faster than it could boil away, except from the surface of the meat and any pockets of free liquids. This could be reduced to essentially nothing by freezing it before exposing it to vacuum. That would be the immediate effect, however it would probably be badly freezer burned over time, so the quality of the meat might be low. In addition, the previous answer raises a great point about it essentially being cooked over and over by exposure to radiation. It would benefit from being in a reflective or radiation resistant wrap, and preferably kept in the shadow of the ship. In the outer solar system or interstellar space, this wouldn't really be an issue since the sun would be little more than a brighter star and it's heat and radiation wouldn't be very significant.
Assuming you are talking about putting a side of beef or a package of sausage outside the spacecraft, rather than processed meat substitute packaged in a sealed foil pouch (which can go anywhere), then what you will end up with is perhaps the worst jerky possible.
The first issue is that the vacuum of space will draw all the moisture out of the meat, dehydrating it. I suspect that the process will be pretty violent, with the water essentially "boiling" out; the temperature will be low but the process will be violent, tearing the fibres of the meat.
Then, the meat will be exposed to high levels of radiation. This will have the positive aspect at first, since it will sterilize the meat, but the end result will be closer to cooking the meat in a badly functioning microwave.
There will also be thermal cooking every time the ship rotates and the meat is exposed to direct sunlight. In Earth orbit the meat will be receiving almost 1400W/m^2 of energy whenever it is exposed to the sun, then it will be rapidly chilled as the ship rotates and the meat is exposed to the cold.
By the time you decide to bring it in and "throw it on the barbie", you will have a shrivelled up bit of something which would resemble old leather. I think at that point I'll reach into the locker and pull out a foil bag of the processed meat substitute, since it will be a lot tastier in comparison...
I recall a story where beef (or something like that) was shipped between planets in the same system with minimal containers and slow low-energy transfer orbits. It relied on the coldness of space to preserve it for months or a year or two during transit.
The long exposure also decontaminated the meat from a disease present on the supplier's planet, it turned out.