Weaning can be traumatic for the foal depending on how it is done. A foal that is weaned suddenly may need some time to settle in before a handler can expect reasonable behavior. This shouldn't be an excuse for bad manners though. It might be best to wait a week or so for the foal to get used to its new situation before asking too much. With the mother now gone an older quiet horse can be a good role model for a youngster.
Weanlings will continue to play and still frequently lay down to sleep.
One behavior that is seen in young horses when introducing themselves to older horses is 'champing' or 'snapping'. The youngster shows submission to older herd members by extending its neck and head, pulling its lips up and back and clapping its teeth up and down as if chewing hard. Through brief interactions and training sessions with humans it is learning to be obedient and trusting.
Horses are referred to as weanlings between the time they are weaned from their mothers and turn one year old. After they have turned one, they are referred to as yearlings. During this time of rapid growth some thought has to be given to the feeding of a youngster. Too much food is as harmful as too little. Over feeding can cause joint problems. A properly balanced feed should be given if pasture or hay are not considered sufficient.
Training should proceed as for a foal. Short sessions of handling and training are in keeping with the youngster's short attention span. If the weanling has been getting grain in a separate stall from its mother, it will already be prepared for spending short periods alone. Standing to be groomed, having its feet trimmed and cleaned and leading should continue to be part of the routine handling a weanling experiences.
Expect some 'bad' behavior from a youngster. Young horses can act out due to boredom with the lesson, frustration from being asked too much or just high spirits. Again, keeping lessons short is important.