There is the Museum of the town living in the center on Uspenskay (Assumption Day) Square. It's small but interesting and has some entertaining exhibits which show vividly how people used to live.
The Museum of Uglich's Kremlin also houses armory, clothes, shoes, cutlery that date back several ages.
Dushegreya (soul-warming clothes, sort of)) was worn since 17th century. I think it used to be a warm comfortable clothing article for a working woman. The climate in Russia is severe and women needed warm clothes, that would not tie them up or restrict movements. This kind of clothes seems to be the suitable one.