You can wear plaid in all seasons. But maybe it would be best....in winter and fall wear a plaid scarf or jacket/hoodie. In spring and summer wear plaid shorts or shirts.
Plaid shoes socks, or anything else will work at all times.
Horses should wear blankets in the winter. If they are allowed to grow their winter coats, something light should suffice. However, if they are being used in lessons or showing and get body clipped,...