Been there done that but it was summer. Depending on whether or not you own the home, you can expect HVAC, the whole setup, to cost around $6500. We just did ours in Late July and after 30 + years the heat and AC needed to be replaced.
If you have a newer AC you may only need to replace the furnace, but it never seems to work out that way.
Good luck,,, we have a few more nights of misery here.
Isn't it special when it goes out when it couldn't get a lot colder LOL!