The snow makes it hard to hike up those hills but it can also cause the birds to move down to where they normally wouldn't be. If you have some lower, and perhaps even flatter ground to hunt, I'd go try that. We've had some good luck late in the year when snow has pushed them down. Try some of the easier terrain where you wouldn't usually expect to find chukar. And I wouldn't worry about killing too many because that's not going to happen! With chukar you need every advantage you can get.