I had a corgi that was way too food motivated to give him treats for training and had to eliminate food treats except for the Come command. It was difficult at first but he learned that I was not going to give him food and still was able to be trained. You can use a leash in the house for the times when he is being too rambunctious. I wonder if you should increase his exercise? He may just need alot longer walks and will settle much better after at least two 45 minute or longer walks a day. That really helped with mine. Also try training tricks at this point because it is great mental exercise. There are lots of methods described on the internet. Use a play session or favorite toy as a reward. Good luck, he sounds like alot of fun.
Oh yeah, the cold makes it harder. With my very active corgi I used to play fetch for about 10 minutes a few times a day. Also, practice the tricks too. My current corgi, Izzy, prefers sleeping and being petted so doesn't need the stimulation.