Great advice. I have ridden in each of those conditions and had to learn the hard way about the pitfalls. Good reminders for the experienced rider and better get prevention for those new to the trail.
Hand and foot warmers, sheepskin ear covers, knee high insulated boots, and wear your chaps to keep wind off your legs. Do not wear cotton pants if it is snowing. Back at the barn, spray warm water under horses hoofs to melt ice balls. Horse will like it if you ride him with quarter sheet. Pull it off his back and up to saddle when cantering so he does not sweat. Do not get horse sweaty in cold weather.