The Access Code says:
The grouse shooting season runs from 12 August to 10 December, with most shoots taking place during the earlier part of the season. You can help to minimise disturbance by being alert to the possibility of shooting on grouse moors and taking account of advice on alternative routes. Avoid crossing land where a shoot is taking place until it is safe to do so.
Grouse moors are common on the rounder, heathery hills of the central and eastern Highlands.