I don't think its nearly as black and white as hot or cold.

If you have frost for a week then it warms back up the woods (food,cover etc.) will be totally different than if it just hasn't cooled off yet. Same goes the other way. If it has been hot all season and turns cold that is much different than if it had been cold all along.

Deer move just fine in the summer. Its more about food and cover than them not liking the heat IMO. The further into fall we go the less food and cover and that means traveling further from one to the other and spending more time looking for food.