I just moved from Montana to Denver... I grew up in CO on the western slope. We only moved because my wife is doing medical school, as soon as she is a MD we are out of here. Realistically it's impossible to hunt during the week, at the very the least living anywhere in the metro area you are going to be 60-90 min to anywhere you can legally discharge a weapon at game, everything close is county owned open space and off limits to hunting and traffic after work and on the weekends has gotten insane. The spot I used to hunt in high school took my buddies 2hrs 30min to get to on a friday night from Denver I now average 5 hours. You will have to go to a range to shoot your bow I have looked around lots and on average be prepared to spend 30 min each way in the car sitting in traffic, spending $10 a pop, and shooting with a crowd. You can set up a target in the national forest for free but getting to a suitable spot at 5pm will take you over an hour one way. Also CO State lands are not public lands so forget any idea of recreating east of Denver.
Also be realistic on how much your new position is going to be paying you the housing in Denver is a joke, 160K might get you a one bedroom apt, any kinda house in a neighborhood within 25 min of downtown will run 450-500k. My brothernlaw sold their 2000 sqft. house for 650k and there were 30 reported shooting on his street in the last 6 months, it was so bad the cops were going door to door and warning residents about precautions they should be taking. The basic going rate in aurora, the cheapest place in the metro to live, for rent on a 1 bed 1 bath is $1300. If you look at cost of living calculators Denver is about twice as expensive as rural Montana so if you are making 50K it would be absurd to make the move for less than 120K-130K even at that high a salary your quality of life wont be the same. I work downtown, live in aurora and we just bought the cheapest apt we could find to save money, so we can save for my wife's school... 138k 1bed, 1 bath, 700sqft. 50 min from work and it took us 2 months to find and I think we got it for a steal compared to what's out there.
Obviously, I'm making generalizations and I'm sure someone is going to say oh that's not true I can get out in 25 min and oh well I got a house with a yard for 300k, but I would be highly skeptical of those claims, and laugh in their face and say when 2012-13 right after the market crashed as the housing prices were just starting to come back.
As someone who is counting the days till I can get back to Montana, all I can say is think long and hard cause you might be getting paid more but I can guarantee you will be looking out that window every day trying to figure out a way to get back to Montana, even for half the pay.