Can I wear a woolly hat in a soccer training session, and can I wear one in a match?
In a training session you can wear anything you want as long as your coach allows it (and why wouldn't they?). Many players wear beanies and other woolly hats or headbands in cold days.
In official matches the Laws of the Game allow certain headgear, but they're not very specific. They're probably o.k., but I've never really seen someone wearing one in official games (sometimes in a friendly I've seen one or two, though)
Where head covers (excluding goalkeepers’ caps) are worn, they must:
- be black or the same main colour as the shirt (provided that the players of the same team wear the same colour)
- be in keeping with the professional appearance of the player’s equipment
- not be attached to the shirt
- not be dangerous to the player wearing it or any other player (e.g. opening/ closing mechanism around neck)
- not have any part(s) extending out from the surface (protruding elements)
5-a-side picked up this topic as well and posted a nice image about it: