I assume that you can do all this with the winnr () command.
winnr () itself tells you the number of the window you are currently in. winnr ('$') tells you the last (bottom) window
The following would return "1" if you were in the bottom window, and 0 otherwise:
echo winnr() == winnr('$')
Taking your example, you could do something similar to do something only in the bottom window:
:autocmd WinEnter * if winnr() == winnr('$')|echo "Welcome to the bottom window"|endif
Caveat: , , , / .