Caribou aren't difficult to kill, but in order to kill them you have to hit them. With a benched rifle, sighted in for the correct range, a 500 yard shot in still air, with no mirage, shouldn't be all that tough. Except that caribou on a frozen lake tend to move across it, they aren't grazing. This suggests that your shot will probably be on a moving target, and a laterally moving target at 500 yards is a demanding shot. If your orientation to the target brings it's movement directly towards or away from you, you will then be shooting the animal on its length rather than broadside or quartering. During the winter put a narrow target out on that lake and see how well you can hit it. Give some consideration to your ammunition. If you handload making up long range ammo isn't difficult (for long range boo with an '06, I'd consider a 130 gr TTSX at 3200 fps) but if you're shooting factory stuff, it might take some experimenting to find something suitable that your rifle will like.
A problem you might not have considered is that of choosing a suitable scope. The cross hairs, in what we charitably refer to as economy scopes, tend to be on the thick side, and at 500 yards might very well block out the entire chest of a caribou. You might have to find a good used scope to stay within your budget yet provide you with a suitable sighting tool for making a long range shot.