Maybe time to hit up some hardened trails. The problem with your local haunt is that it really doesn't respond well to rain.
I mean, you could but a fat bike or something, but those I know with them say they're shit in the mud anyway. Maybe become a mudroadie?
Slade actually drains pretty well, with only a couple of small areas that remain underwater. And FUCK buying a fat bike because I'm not a brodude, or a dudebro, or a ponce. And mudroadies are basically mucky Jimmies.
Do you have good enough clothes? This winter, I got good water-proof cycling pants, shoes and warm gloves. Just those three things make all the difference, and I can go out no matter the weather. In theory. In practice, maybe once or twice a week. But still!
Good enough, I think. Two sets of bibs so the local ladies can gawk at my magnificence and a waterproof jacket. I don't really feel the cold or the wet when out on the bike.
The shiniest bike you can find. And maybe something a bit different to what you're used to.
I have been considering it, but I know I don't actually neeeeeed a new steed, so I know that once the novelty wears off I'll be filled with buyer's remorse.
I think I need to get over the feeling that going for a ride in winter is a hassle, ie longer to get dressed, longer to prep the bike, longer to clean and maintain the bike afterwards and more clothes to launder. I know I'll enjoy myself tremendously when actually out on the bike - I hold this truth to be self-evident. I think the problem is over-thinking the actually doing of it.
TL;DR: I'm getting lazy in my old age and the sofa is like super-comfy.