I don't know about latex to answer from its side, but I don't see a setting to make Vim look for the path with extensions, so you will have to create a custom mapping. Unfortunately, there are no command-line equivalents to the gf and f style of commands, so you have to mimic something equivalent (sorry, untested).
function! OpenFile()
try
exec "normal! \<C-W>f"
except
if filereadable(expand('<cfile>').'.tex')
split <cfile>.tex
endif
endtry
endfunction
nnoremap <silent> <C-W>f :call OpenFile()<CR>
You can put this in an ftplugin (with option for nnoremap) to restrict it to your latex files only.
Note: If you want to cover different cases such as gf, F, you will need a more sophisticated function, or just write different functions for each.