Nope
Does wood take longer to dry if it is inside a garage? Here is my problem I just got a 10 cord logger load of oak mostly red oak and it is fresh cut green. I hope to get it all cut up and split by the end of October, I either want to build a open air wood shed meaning no sides and put where it will get plenty of wind or I have a huge garage I can clean out one stall and stack the wood inside the garage but will it be dry by next October inside the garage with no wind, or much air circulation? I keep the garage closed so the critters don't get in. I know red oak takes a good year to season.
Nope, it won't dry well in there, not with the door shut all the time, and it won't get good airflow regardless. Dry it outside, and then just bring in a week or two's worth in heating season. That'll give ya a chance to knock more junk and dirt off the pieces before they enter the house, as well as making it convenient to go get a few sticks. If you have the resources to build an outside woodshed..do so!
Besides man, you need your space in the man cave! Don't want to fill it all up with firewood, that's a waste!*** You'd regret it within weeks of doing that.... Need workbenches and that old classic to have a place to be parked while you work on it, the lawnmowers and other gear, place for your table saw and who knows...that stuff, and you will accumulate it. Mancave is for working on projects with tools, and for keeping your ride dry, it ain't a closet....
***Unless you are talking "jay leno" sized garage, then go for it, all your firewood, park your yacht in there, your planes, fleets of rides, indoor target range, miniature golf, olympic pool, etc.