Sure it can be done. I never used this feature, so I'm not sure whether there's an option for "a simple icon", but you should take a look at the "bookmark widget":
First, start your browser and create a bookmark for the page you want to link to. Second, go to your homescreen, long-tap on a free space (where you want the link to be), select "widgets", and then watch out for the "Bookmark widget". Tap it, select your bookmark, et voila! there should be a shortcut on your homescreen.
Alternative to the second step: while still in your browser, go to "bookmarks", long-tap the bookmark you created, and select "add to homescreen" (source: AndroidCentral).
To do the similar thing to open a file with an associated app, depending on the launcher used, explained using an example:
- Go to your homescreen
- Long press an empty space where the icon should be placed
- In the opening menu, select "shortcut"
- Select your file manager (this won't work with all file managers; in my example, I used ES File Explorer, which perfectly serves this case)
- Now navigate to the file you want to create a shortcut for (in my example, I selected an EPUB ebook)
- The icon should appear on your homescreen.
Now, tapping that icon, either your ebook reader opens directly (if only one is installed, or you've made it the default to "always use"), or, as in my case, a popup asks you to chose the app to be used (e.g. Aldiko, Moon+ Reader, FBReader).