It is always a good idea to bring boots into your tent at night.Aside from insects, snakes&critters(including bears that can confuse your scent&the mink oil-treated leather for a meal), frozen boots are uncomfortable to deploy in the morning. Also freezing is hard on wet leather.
Incidentally, I have mistakenly tried "drying" my boots near a campfire for several hours before turning in, only to find permanent cracking and shortened life of the boot.Stuffing clean dry socks will speed drying overnite. Like dirty clothes,waders, food and uncooked utensils, I try to avoid bringing these into a tent at night in mountain country, preferring to store them well away from sleeping quarters or in a vehicle if accessible. Placing them inside a sleeping bag may work best. But I am also cautious, always choosing to travel with a rimfire device in case of unwelcome visitors.