Hej! Sweden has a lot of compitition and hunting, no local carry for self protection. Most of the real Swedes I know (at least all my relatives still in Sweden) shoot and/or hunt. I don't know any real "anti-gun" sentiment.
As for laws in the US: It is legal for you to loan him any of your weapons if you want to hunt or go to the range. Here in WA it would be legal for him to purchase his own if he is in country legally. He would also be able to carry a pistol with a special (shall issue) permit, but as he is not in WA you will have to check your CO state law on that part.
There is no federal national restrictions that I know of, all different states, different laws...I do know as a non-us citizen he would not be able to purchase a handgun in NYS, but then that is NY and not the US. (I know the NY thing because I was still a legal alien when my FIL gave me my fiirst pistol (in NYS) and had to get it out of NY and into PA quick. (and this was even before the GCA 68))