This sounds very familiar! I recently moved to a new house and I have 2 minis, one long haired and one short haired. Gus, the SH, is 6 and I've had potty problems the entire time I've had him. He holds his poo when it's cold and rainy and also marks furniture in the house. I've tried many different methods and a found that a combination of things manages his behavior.
I live in Texas now so it is probably not as cold or snowy as your house but some of these things might help:
When I'm home, if I can't see him I am assuming he is marking something. I keep blankets and beds in all of the rooms so I can keep track of him when I move around the house. He will usually follow me from room to room anyway, but will leave if he can't lay down and be warm. When I leave the house I shut every door to the extra rooms with carpet, he really only likes to poo on carpet. He has a bed that is like a pillow with a pillow case he can climb into and be warm and covered. He does all his marking when he thinks he is alone.
Mornings are the hardest part because I don't want to spend 30 minutes standing in the yard making sure he goes. I let them out after I shower, about 15 minutes after I get up. I found that if I let Gus out first thing his body hasn't had time to register the potty urge, so I give him a few extra minutes to wake up and have a drink. If it is cold, snowy, or rainy or he ran back to the door too quickly,I just assume he didn't go on the first try, so I have my SO let them out before he leaves , about 30 minutes later. My SO will walk around the yard with them and it usually triggers the business. I have found that I have to keep him moving in the yard. If he has stopped to stare at me, he is not going to go. I have to walk around with him or say "kitty" to get his mind off the cold and force him to move. If I am in a bind, a short walk will work for us or some play time. I think the key for Gus is to get moving and then the urge will become worse than the cold. He sits in his warm bed all day hibernating, so whatever movement really makes it more managable.
I also bought a spot bot for "accidents". Good luck, I know it's really frustrating. I have yelled "just go! We all know you have to go!" So many times.