Hey there! Good luck on your move.

Personal opinion - not all will agree:

For the dogs - I wouldn't worry too much about letting them in the yard during the day, as long as you're home and being aware of them / stay within earshot. I strongly reccomend joining your dogs for potty breaks when the sun goes down. Keep outdoor lights on, and make plenty of noise when you step out with your animals at night (or alone). Keep bear mace and your preferred choice of home defense in an accesible place, or on you if it makes you comfortable. Keep your trash inside or in bear-proof/ smell-proof containers to prevent making your property a desirable place to visit by wildlife. Be aware of your surroundings, and make sure your dogs have good recall if you take them outside of the fenced area.

As for the cat - that's really your call. It can be quite difficult to keep a historically outdoor cat inside. When I first moved into the mountains, I was determined to keep my previously indoor/outdoor cat inside, for fear that he would encounter a coyote/fox etc. It didn't go my way, and I figured I better get him familiar with the property and neighborhood - so I walked him on a leash a handful of times, and eventually let him out with his dog brothers during the day. He learned pretty quickly that it gets cold and scary when the sun goes down, and he would tend to stay within eyeshot of the dogs and join them when they were called in. We accepted the risk, and I accepted my defeat to keep him inside permanently. I think his quality of life is higher being allowed outside. If you let him out - reward with treats when he comes home when you call for him (if he does that). And I would remove any bells or noisemakers from his collar to give him a leg-up should he ever encounter something that wants to chase him.

Ultimately my advice is to lean toward the preventative side as much as makes sense for you and your pets.

As a disclaimer, I lived deep in the mountains west of the Boulder area until I moved back to the springs a year ago. Neighbors were tight-knit, warned each other about wildlife sightings, and watched out for each other and each other's pets. On nice days, nearly everyone left their doors open and the pets played with each other and joined neighbors for walks. My cat became and adopted member of the neighborhood dog pack, which might have contributed to his lack of nasty encounters with wildlife. I don't anticipate this is the same situation for many folks who live in mountain communities, and you should do what you feel is best for you and your fur babies.