Probably to a small extent but the more pronounced effect is the heat gradient. The rest of the house becoming quite a bit colder just sends you back to the fireplace, which is generally not a bad place to be, so overall it's not a major issue.
It does, and it creates a floor on the outside temperature where the heat from the stove is overcome by the losses of sucking in the cold air. This depends on the design of the stove. Some wood stoves pull down the firebox air from the outside to avoid this problem, but it is fairly unusual. There is a second heat exchanger with its own fan that circulates the inside air. The problem with this is that you still lose a lot of heat up the chimney.
> Some wood stoves pull down the firebox air from the outside to avoid this problem, but it is fairly unusual.
AFAIK in europe having outside air intake in stove is mandated by law. You can not use it, but all newly built houses have outside intake if someone was planning on adding wood stove. You also need to have proper vent near your stove, so even if it uses inside air, it will typically get it through that. I have automatic pellet burning furnace in basement for normal heating needs (it starts automatically when needed, uses 3 temperature sensors on floors and in basement) and wood stove for "romantic" purposes, but when it's fired, it heats up almost whole house and pellet stove sees that no more heating is needed. I have lots of leftover wood from construction phase, so wood stove will pay itself back from reduced use of pellet.
As for losing heat through chimney - properly mounted and operated wood stove doesn't lose that much heat through chimney. Most of them have long enough steel pipe from stove to chimney, which reuses some heat from exhaust and ventilation channels in chimney, which are heating incoming air.
Many fireplaces that HSE outside air sometimes put hot smoke out the intake. The intake probably wasn't designed for this so it is a fire hazzard. This can be avoided, but if you don't know how you probably didn't.
Then again Ben Franklin figured out how to make a fireplace that worked yet most don't.
