The alias is just a pointer to the actual item you want to get to, so its icon can be anything you want. To change the icon to something else (say, a folder icon), do this:
1. Click on Finder Desktop (Finder name will appear in the top Menu Bar just to the right of the Apple Menu).
2. Go to File Menu and click on New Folder (or press the key combination displayed next to it). This creates an empty folder on your Desktop.
3. Click ONCE on the New Folder on the Desktop to highlight it (not DOUBLE CLICK, which will open a window of its contents).
4. Once the new folder is highlighted, go back to the File Menu again and select Get Info (or press Command-I). This opens a window displaying information about the folder. At the top of this window is the icon the New Folder is displaying on the Desktop. Click ONCE on it to highlight it, then go to the Edit Menu at the top of the screen and select Copy (or press Command-C). This copies the icon to the Mac's Clipboard.
5. Click back on the Desktop, then click on the alias you created whose icon changed. Select Get Info for this alias, which will again open a window displaying info about this alias. Click on the icon for the alias at the top of this window to highlight it.
6. Here's the good part. You previously copied the icon of a New Folder you wanted to use for your alias to the Mac's Clipboard. Since you've now highlighted the alias' icon that you no longer want to use, you can change it by simply going to the Edit Menu at the top of the Finder Desktop and selecting Paste (Command-V). This replaces the alias' icon with the one you previously copied to the Clipboard.
This works with all the Mac's file/folder/hard drive icons. Find any icon you want to use, copy it to the Clipboard, then do a Get Info on the destination file/folder with the icon you want to change. Select the destination file/folder's icon at the top of that window and paste the icon you previously copied to the Clipboard. You can move the New Folder you created to copy its icon to the Trash when you no longer need it.
I've used this technique to change my hard drive icons to ones I like better than the generic one the System uses. This is purely a cosmetic change and in no way affects the functionality of the object whose icon you changed. If you find custom icons on the Internet you want to use, be sure to save them somewhere, because if you ever erase your current hard drive the icons may revert to their default icon. Also, be sure the name you give your alias object it not the same as the destination object itself. You don't want to get confused and move/delete/trash the real object later (just click on the alias' object's name, and type to rename it to something like Alias to Time Machine).
Have fun.