You have all my sympathy, but I don't think what you're feeling is unusual. I lost the dog of my heart 5 years ago, and it took a year before I was back to normal even though I still had 2 other dogs. The reason I have other dogs is that I found years before that I am one of those who grieve. I went years without a dog between my first and second Akita. Sometime after that I decided I'd always have 2 dogs of different ages so I had an emotional bridge and didn't go without for years again.
So I haven't gone without a dog again, but as above, I have grieved to where it affected pretty much everything in my life for a pretty long time.
I'm considerably older than you are, and I now have a puppy. He'll be the last. Raising him is a joy but also more physically difficult that any other puppy, and he's of a smaller breed. The loss of sleep in the first weeks was especially hard - and he's a good puppy. He started out sleeping 6 hours straight every night. Our circumstances are undoubtedly different, but my theory is having him keeps me up and at 'em. I hope to still do Rally and Obedience competition with him. My one remaining older dog is having medical problems that I think have put an end to her competitive career.
I understand your concern about walking a dog in winter. I'm fortunate to have a fenced yard. In bad weather the dogs don't want to go out or walk. They zip out, relieve themselves, and zip back inside. Particularly if you get a small dog of one of the companion-only breeds, I don't think skipping anything past a potty walk is a problem in bad weather or when footing is worrisome. If you have a fenced yard, where a dog can go out for a bit by itself, it wouldn't be a problem at all.
So if you want a puppy, try looking for an older one. My guy came to me at 11 weeks. The Akitas were 12 and 16 weeks, respectively, and the older, the easier in my experience. If an older dog would suit better, try for a foster to adopt situation. Good luck.