There are two separate reactions going on Bill, polymerization and drying. The polymerization of linseed oil is greatly enhanced by exposure to UV. To get UV, you need direct exposure to sunlight, as glass does not transmit UV (that’s why you can’t get a suntan indoors). UV can get through clouds; the thicker the clouds the less that gets through. Someone did an experiment using black lights to try and speed polymerization of linseed oil indoors. As I recall, they were not successful. You could probably find that thread in the old archives.
Turpentine, if you have any in your varnish, actually dries, in the sense that there is a volatile component that leaves the surface. I would guess that the drying rate of turpentine is primarily mediated by temperature.
High humidity reputedly slows polymerization, but since I live in the West, I have no direct experience with humidity.
To answer your question, linseed oil varnishes will dry indoors, albeit more slowly that if they have some sunshine. I just put a coat of varnish on a gunstock, so of course it’s snowing. If y’all have any extra global warming where you’re at, I wouldn’t mind if you sent a little my way, at least until I get this stock finished. Then it can go back to snowing for all I care.