▪ Wash the insole separately if you’re able to remove them. This will help make the inside of your shoe fresher. Laces can be washed or just replaced.
▪ To remove surface dirt such as mud and grit, use an old toothbrush, a little warm water and a gentle, anti-grease soap. This should take care of the dirt, and is fine to do once in a while.
▪ Dry your shoes naturally, and don’t place them near a radiator as direct heat will alter the shape of the shoe. Open out the shoe and then stuff the inside with kitchen paper or newspaper. The paper absorbs the dampness inside the shoe. A shoe takes about twelve hours to dry out completely.
▪ If you’re a frequent runner, you may want to use two pairs of shoes for winter running, then you can alternate between them as each pair dries out.
How to clean your running shoes (asics.com)