Actually, zinc oxide is one of the worst things you can put on true scratches. It softens the skin and makes it more susceptible to allergens and irritants.
What you want from your vet is a combination steroid and antibiotic cream, water based not oil or oxide based. Then clean the scratches well with plenty of water and hibitane (fluorhexadine) and dry them very well. Apply the cream topically twice daily and clean the legs sparingly (I find once every 3-5 days to work well).
It is also useful to find out what the cause of the scratches is. Some horses it is allergens to hay or grain, some horses it is zinc/copper deficiency, others it is standing in mud, etc.. so try some things out and make sure your horse has somewhere dry to stand come spring.
They say money doesn't buy happiness -- well happiness doesn't buy horses!