When we came to the UK over a year ago I had no idea how to dress my children warmly.  Now with a little trial and error I can dress my toddler for hours of outdoor play in almost freezing conditions. Mixing in with other families I have found that most locals use a one piece padded snow suit and in warmer weather a one piece splash suit. We found the snow suits too restrictive and found the splash suits too sweaty. So this is what has worked well for us week after week.

• Wool hat. Otto will often remove it but we always start out with a wool hat on. We love the hats made in Australia at Typically Red. 
• Wool Coat. We wear as much wool as we can as it breathes and it repels water. If it is raining heavy we will get under the shelter but we've found the wool coat provides warmth, soft comfort and water protection. We love this coat so much we already have the next size up for next year. 
• Wool and cotton layers. Otto usually wears two to three tops, the layer closest to the skin is always wool. The layers trap warm air and it allows Otto to still have some warmth if he takes off his coat, which he often does. It's all about the layers. He wears wool leggings as his base layer on his legs. Most of his base layers are Engel, Disana or Cosilana. On the coldest of winter days Otto wore his Disana one piece wool suit under his bib and brace. 
• A fleece lined bib and brace that is insulated, windproof and waterproof to 10000mm. This is really key to making all of the layers work. It is also soft not scrunchy or rustly. 
• Wool socks.
• Rain Boots/Wellies, often Otto wears waterproof wool lined snow boots. In the middle of winter I found while undressing him that his whole body was nice and warm except for his feet. The wool lined snow boots were a game changer. 

Otto loves to play in mud and often you cannot see his boots, so water proof shoes and suit are important for his comfort. I found this clip useful, it is adorbable;

For their school Forest School Class my older boys wear a coverall over their uniform. When they come to Otto's Forest School class (usually during the school holidays) they wear water proof pants over their base layer and a coat. Otis (8yrs) love the Demar boots (UK only link) as they are fleece lined but are amazingly light.

I'd love to hear how you dress for Forest School or general outdoor cold weather play. Perhaps your Forest School has a unifom?