there are many way:-
1.You use to query string for apply themes.
2.You find control of previous page dropdownlist control and selected value apply.
3.Best way you use session. when user change the dropdownlist value is store in session variable. now you retrieve session value in any page and apply the themes.
4.you store the user themes in database. and when user login then retrieve value form database and apply in each page.//this use for when you write a program for authentication base program.
I hope my suggestion is helpful for you.