I should have mentioned my kids ages, I meant to in the OP and got sidetracked. My daughter is almost 3 (February birthday) and my son is 5.
We moved from Florida to Nova Scotia when my daughter was 5. She and I spend a lot of time outside, even when it's cold. Here are some of our favorite things to do:
1. Sledding - This might not be great since you don't have a lot of snow, but when you do have snow sledding is great fun. We spent a little money on sleds and snowpants, but it's free after that.
2. Hiking - I love hiking in snow, but it's also fun when there isn't snow. Undergrowth is cleared, so some of the trails by us that are impassable in the summer open up. Insects are non-existent. On really cold days, we like to go down to the creek in the ravine behind our house and find ice to smash. If the trails are icy, we use yaktrax (or similar).
3. Ice Skating - We have an free outdoor rink (weather dependent) hosted by the Lion's club and an indoor rink in town that has free and low-cost sessions a few times a week. Our daughter also does a low cost "skate club" that is quasi-lessons led by some women on the college hockey team. Lots of folks around here do hockey, which seems expensive. I like skating, but it's tough on my ankles so I usually just watch.
4. Snowshoeing - We've only done this a few times, but it was pretty fun.
I totally agree with you about biking. I love biking, and do a fair share of winter biking, but I wouldn't call it fun, nor would I try to sell my daughter on it. :)
So my son is just now approaching the age where hiking is fun for him, but my daughter is in an awkward stage where she's too big for the backpack carrier but doesn't really have the endurance to hike more than a quarter mile or so. This past summer, we got half a mile into a hike and my daughter decided she was done and I had to carry her back to the car on my shoulders and wait for my wife and son to finish up the 1.5 mile loop.
We don't really get enough snow for sledding and snowshoeing, we typically get one "real" snow per year where its more than a dusting and its gone within a day or two.
Ice skating is a good idea though, my kids might enjoy that. I'm not sure about my daughter, but I have heard of little ones ice skating.
As for biking--I actually don't mind riding in the cold as long as its not too windy, a lot of that is related to the fact that I've been cycling forever and have really nice gear for the cold. They just don't seem to make good kids warm clothing. The gloves that I have give pretty good dexterity and are comfortable to ~20F or so, my kids have the option of knit gloves that give enough dexterity to grab a handlebar but are only good to ~50F or so, or mittens that really are useless for anything that's not riding a sled.
See if your local library has a season pass to check out for ski or tubing access.
Wat?! This is a thing? I'll have to check that out.
We really enjoy visiting public pools with slides, diving boards, play areas, etc during the winter time. As a bonus, I love knowing that my kids are capable swimmers and visiting pools frequently has naturally made them proficient without professional instruction.
This is not a bad idea. We have a YMCA nearby with an indoor pool. My kids aren't super confident swimmers yet, but maybe this is the chance to work on it. I never really thought about swimming when its cold out, but if its inside, why not?
My kid loved the following activities when she was a preschooler. She's 10 now, and she still loves the following outdoor activities...
- Sledding
- Skating (not necessarily with skates; she likes just slipping and sliding around on the ice)
- Winter hikes, with or without snow
- Playing at the playground
And also the following indoor activities...
- Going to the library
- Going to a paint-your-own-pottery place
- Reading books
- Baking cookies
- Playing board games
- Making puzzles
- Swimming
- Indoor playgrounds
- Indoor trampoline park
Hmm, good list there. Our indoor playgrounds and trampoline are not super cheap--the indoor playground is 15/kid and the trampoline place is $25/kid, but I guess that's cheaper than skiing and doesn't require specialized gear. The sedentary activities are not really ideal for my kids--it seems to really tax them emotionally when we do stuff that doesn't involve heavy physical activity, they end up exhausted and bickering if I don't get them running around for a good part of the day.