I have always felt very strongly about horses having a decent warm up and cool down when exercised, i think even more so in the winter months.
I have to be very careful with my mare due to her PSSM doing to much to soon with her PSSM could cause a tie up if her muscles are not warmed up adequately before exercise, I do the same with my gelding and all other horses I ride. 
All horses are different you get to know your own, some horses could take 20 minutes plus to be warmed up where as others 10 minutes suits them. 
A proper warm up and cool down reduces the risks of health problems in your horse. It allows the muscles to loosen up naturally and less strain on the tendons, i t allows more oxygen flow and better circulation around the horses body. The warm up physically and mentally prepares your horse for the work load ahead but it's important your horses fitness is up to that level of work.

It is important especially at competitions not to warm your horse up to soon or do to much to soon as you do not want to exhaust them. Rugs help in-between especially in winter months to avoid tightness of muscles and getting a chill. 
The cool down must be of adequate time for the horses pulse and respiratory levels to return back to normal and also to prevent health risks such a colic,chill and overheating. 
It is beneficial in the winter months to have your horse clipped depending on work load and how much coat they get so you can cool your horse down effectively. If your horse has a thick coat and you struggle to get your horse dry before he gets cool to rug him then it would be worth looking into a clip. 
All year round I give my horses salt, it is especially reccomended for horses that are exercised and in hot climates as alot of salts are lost with sweating. Electrolytes can also be useful. Even if you give salts licks horses usually wont take in the amount they need. 
It has been researched that in the summer months it is better to not use a sweat scraper when you have hosed of your horse as it doesn't effectively cool them down. Dr marlin has shared his research on his page on Facebook there is some useful information on there regarding the cooling down of horses and the importance in more detail.