Welcome to the forum Emma. You will find a lot of owners with dogs, one mad Welsh chap even takes a cat to Spain [He'll be along soon]
Insulation is fairly good, and the large gas fire can easily cope with low temperatures. You will get condensation around the aluminium trim that edges the roof in cold weather, but that takes a minute to wipe down.
Size wise I'd advise a Troll so you have enough space for the dog to stretch out. You do not need a large car to tow these larger Eriba's and will find something Golf size will do the job. If you have a budget in mind I'm sure members can point you in the direction of suitable vans on the market.
Colin