The problem with plain HTTP is that its just for retrieving content. There's no concept of folder or file list.
Some web servers let you browse directory structures by generating nice HTML pages with links to files for directories. And at least things like
lftp are able to parse some of the common formats those indexes are generated as and give you the impression that it is a file transfer protocol, but it's not really, and I don't know of any fuse file systems that can parse indexes the way
DAV is an extension that just does that and is already covered by jordanm's answer.
But note that if you don't need to list directories,
avfs at least can let you access web pages over the filesystem.
$ mkdir AVFS
$ avfsd AVFS
$ grep -w Reputation 'AVFS/#http:unix.stackexchange.com|users|12583|javano'
<span class="count">731</span> Reputation
Now also note that you can install
sshd (via cygwin) or a FTP or Apache with DAV on a Windows machine as well, so you should be able to do the same things as you do on Unix machines.