Space isn't really cold. Or hot. Those things just don't really make much sense in space. Temperature is a property of matter, and there's (practically) no matter in a vacuum. So space isn't cold.
Objects in space have temperatures that are solely dependent on what sources of radiation they are receiving. If you're in a space near a star, you could be hot even floating in space. On the ISS, the metal facing the sun can get up to 260 C while the metal in shadow can cool down to -100 C.
So it all depends on the local environment. Our own asteroid belt ranges around -73 C to -108 C. In another system where it was further or that had a different type of star, it would be hotter or colder.
All of this is to say that being in an "ice field" or whatever wouldn't really affect what the temperature of your ship was. Main thing that would affect it is if any objects put you in the shade. Though if you ARE in an "ice field", that's because the amount of radiation reaching there is at least small enough to make it below 0 C.
But as someone else said, real asteroid belts are not in any way dense. We've sent plenty of probes cruising through with no problems. They say the odds of you getting hit are less than one in a billion.
Similiarly, nebulae aren't anything like they are typically depicted in scifi (including FTL). If you were in a nebula, you probably wouldn't really be able to tell.
But none of that is much fun.
