In reply to Dave the Rave:
For a full day in winter (bearing in mind I've not got the skills to take us where ice axe and crampons are needed) my 14 year old son would take:
Salomon boots (not budget, but they were what fitted)
Dare2b thermal top and leggings
Craghoppers walking trousers
Peter Storm overtrousers
Craghoppers long sleeved base layer
Rab Boreal windtop thing (got it in a sale, I've got the Aurora, which is the women's equivalent)
Craghoppers fleece
Craghoppers Compresslite Packaway insulated jacket
Mountainwarehouse waterproof jacket
2 pairs of one size Mountainwarehouse gloves for use as liner gloves, one to have one, one spare
Mittens (Sealskinz I think) or Lowe Alpine Waterproof Gloves
Peter Storm neck gaiter
Peter Storm fleece hat
Katoolah Microspikes
Alpkit head torch
When we were in the Brecon Beacons in snow my sons took one each of my husband's cheap walking poles, can't remember the brand.
My son very rarely wears the overtrousers, the walking trousers over leggings are way more comfortable. But they're obviously necessary to have with us. Other than that, things get pretty well used.