Cookie path and its accessibility to subfolder pages

If we set the cookie to path '/subfolder1', will the cookie will be made available to any page or subfolder beneath the folder?

Yes. The cookie will be available to all pages and subdirectories within the /subfolder1 path.

To remove some ambiguity by reusing a portion of this answer:

A request-path path-matches a given cookie-path if at least one of the following conditions holds:

• The cookie-path and the request-path are identical.
• The cookie-path is a prefix of the request-path, and the last character of the cookie-path is %x2F ("/").
• The cookie-path is a prefix of the request-path, and the first character of the request-path that is not included in the cookie-
  path is a %x2F ("/") character.

There is a slight (but potentially important) difference between setting a cookie on the /subfolder1 path and the /subfolder1/ path.

If you rely on the former your request path needs to start with a "%x2F ("/") character" (a forward slash) to guarantee the desired behaviour. For an example, take a look at the linked answer.

Setting the cookie path to simply / avoids any edge cases, but as you say - the cookie would be accessible the entire domain.