@Davon Lowery Doesn't it take 10 hours just to get out of LA? haha!
Seriously though, SLC proper is 9.5 hours according to google maps. There's some canyons up this way that would fit the criteria. You would never want to buy anything up a canyon without water rights. If they dont come with the property, they're really hard to get and can cost up to 80k depending on the canyon.
Depending on how remote you want - Millcreek canyon has some places up for sale in the 200's. Check the utahrealestate website for the Porter Fork area. It's very remote (I think only 50 cabins up there) and it has tons of hiking trails and a stream right out your front door. In the winter, the road is only accessible by snowmobile though (at least that's what I hear). but the main canyon road is accessible. They also turn the last 7 or so miles of the road into a snowtouring road (no cars) from Nov-June. So that's very cool. These cabins are on leased land from the national forest service though, so they have to be bought cash.
Aside from that, emigration canyon is nice, but you wont get a place for under 450k. Big & Little cottonwood canyons have the ski resorts up them, but expect to pay for that (again, around 450k bare min for a house). You may find a condo at solitude or snowbird for the mid 200s, but it's not going to be the remote cabin feel obviously. Will be very easy to rent out though.
All of the above places are 30 minutes to downtown SLC, so having a property mgt company check on it shouldn't be an issue.
Moab, UT may be another option. It's not really the mountains, but an awesome area. Dont have to deal with snow either.
Hope this helps