The weather can definitely make the hunting far better. I know going into my 2nd season hunt this year, I was sure thinking it was going to be a looooong, tough hunt with it being so warm, dry and sunny. With those conditions, old bucks (and even most deer) just don't move around much. Too darn hot wearing coats rated for -30 degrees. Days on the mountain can be real long when the bucks are bedded up in dark timber all but 45 minutes each day.
Snow, cold, even just some overcast can change things big time. I was telling my wife that I'd rather hunt just 2 days after a big storm than 9 days of dry, warm weather hunting.
Luckily for me on my 2nd season hunt, I knew exactly where a taker lived and could be in just the right spot during that 45 minutes per day that I had. And then the day of rain and overcast helped a lot......kept him in the aspens, rather than him moving to the dark timber 30 minutes after first light.
The bucks in Colorado will be rutting late in the 3rd and during the 4th season though. They won't be as active if that sun is shining and it's warm like it's been, but it'll still be good hunting. They might be scattered too if there's no snow up high. I think some will migrate regardless, but many at least need some snow to move them.
I wish I was headed over there to hunt or spot during the 4th. Sounds fun in a good unit. My wife had a 4th season elk tag and I was excited to go with her, but she returned it when I was in bed in pain with my hurt back.