Winchester is not unusual in the Banff/Moray area. It is possible that people with the name are descendants of the 15th century Winchester, but an ancestor may have adopted the name or be a descendant of another person.
Possibilities are:
1. Look in the on-line catalogue of the National Archives of Scotland and of the National Archives for Scotland (on the same site). Key "Winchester" into the search box and see what comes up.
2. The same site will tell you what church records (parish registers, kirk session minutes etc) survive for the area.
3. If any of the Winchesters owned any land, they will appear in the register of Sasines.
4. The book "Fasti Ecclesiae Scoticanae Medii Aevi" will give deatails of pre-Reformation churchmen.
5. The Register of the Great Seal is very much worth looking at (this has been published).
6. The Register of the Privy Seal (again published) could be useful.
7. The Registrum Episcopatus Moraviensis (published) mentions a Jaspar Winchester who was a tenant of the Bishop of Moray in the 1560s.
8. There may be Winchester wills (index on Scotland's People and can be downloaded from there for a small charge).
9. Other odds and ends e.g. the Acta Dominorum in Concilio.