To change an existing tileset to another (completely), make sure "Use Custom Tileset" is unchecked, then select Ashenvale and accept. It'll switch your tilesets. Save it before you do it though, just incase it doesn't go well.
Or are you asking for something else?
Some tilesets are locked. This is because they're used in cliffs (and somehow Blizzard doesn't allow cliff tiles to be replaced).
And coincidence (not really) wills it that this guy asks for a cliff tileset to be replaced. You'd know this if you had read the thread.
Unfortunately, you will have to create a new map for this and use the tileset of your wish (ashenvale, probably).
I tried JNGP's "edit tileset" (which used to work, but it doesn't now for some reason).
Firstly, change all tilesets so you've got the set you like.
Then go to your old map, export all trigger and object data. Highlight the entire terrain (just dragging will do) and press CTRL + C.
Now go to the ashenvale map, press CTRL + V and the terrain should be... about the same (do the same for all pre-placed doodads and units.
Then import all object and trigger data.
NOTE: If the map is really large, dividing the terrain in 4-9 different sections would be a good idea.