The ski season at Norus runs from roughly January through early March, though the exact dates depend on snowfall — in a poor snow year the lifts may not open at all, so check locally before making the trip from Bishkek. Weekends are busy with Bishkek families; if you want the slopes to yourself, come on a weekday.
Summer (June to September) is a different kind of reward. The valley turns green, wildflowers cover the upper meadows, and temperatures are mild — warm enough for hiking in a light jacket, cool enough to make the effort pleasant. The Ysyk-Ata thermal resort up the valley stays busy through the summer with city visitors escaping the heat of the Chüy Valley floor.
Spring and autumn are quiet and can be muddy. The mountain road is passable but less inviting.