If just in the rain, you might want to try what cold water paddlers use. I have a couple of different kinds of gloves that work pretty well for race training in colder shoulder seasons. Mits are also available for more protection and warmth. Do a search for "cold water paddling gloves". Most are not great for truly cold frozen ice conditions, but for above freezing temps you should be able to find something that works for you.
Just as a follow up to this idea, I wound up ordering a pair of NRS Catalyst gloves. I went out today for about a 35 minute walk (47 deg F; steady but not overly heavy rain; no wind) and have to say I'm thinking this was an awesome suggestion. Hands were very comfortable even though I was walking pretty slowly so I wasn't heating up like I would hiking. Totally dry. I was even pleasantly surprised that I was actually able to operate my phone with the gloves. I assumed that was not going to be an option. It was also fairly easy to use the zippers on my jacket pockets, use the unlock button on my keychain, etc. Seem reasonably functional which is a huge plus. There is also enough room with the size I got that I'll be able to get a thin liner glove inside and also the Pertex liners I have for my OR 2 in 1 gloves appear to fit over them, which would make them warmer and even more impervious to truly foul weather.
On the downside, the major issue is that when they get wet they definitely stay wet. They've been hanging on the coat hooks in my entry for about an hour now and they're still very damp. In my case that probably won't matter because they'll generally be for day hikes so when I'm done I'm just flinging them in my trunk, not trying to figure out how to dry them in a tent on a cold, damp night. The fit is also a bit off. The overall length is perfect for my hands and correlated perfectly with their size chart. The pinky finger however is a bit long and when I clench my hand I get a fold at the base of the palm there and about 1/2 inch of space opens up over my pinky. The size chart matched my hand circumference perfectly here too but they definitely appear to run big in that way. The model I went with was only 2mm neoprene and the fingers are "pre bent" so not sure if that was a factor or if this is just normal for this kind of glove. The heavier waterproof and insulated gloves were all at least 3mm neoprene. NRS was a company that seemed to come up repeatedly in "best paddle gloves" searches so I'm assuming it is one of the better brands for water sports but I have no idea on that either.
Looking forward to trying them out in colder, wetter weather but I think these are going to be perfect for what I was looking for. Thanks for providing an alternative perspective on my question. That's why I love this forum. Recommendations received here always seem to be spot on.