When trying to automatically open the corresponding .cpp or .h file using autocommand I encounter no colorscheme on the corresponding file that is opened. I'm not too familiar with vimscript but I believe Vim is opening the file thinking it is of file type ".txt" and therefore using a default colorscheme.
Two autocommand lines in ~/.vimrc:
au BufRead,BufNewFile *.cpp exe "bel vsplit" fnameescape(expand("%:r").".h")
au BufRead,BufNewFile *.h exe "vsplit" fnameescape(expand("%:r").".cpp")
Any help would be appreciated.
Your answer is a workaround (though you should use :setlocal instead of :set to avoid that the syntax leaks out to new buffers that are opened from that one), but it doesn't attack the root cause, which you'll find explained at :help autocmd-nested:
By default, autocommands do not nest. If you use ":e" or ":w" in an autocommand, Vim does not execute the BufRead and BufWrite autocommands for those commands. If you do want this, use the "nested" flag for those commands in which you want nesting.
Syntax highlighting (you say colorscheme in your title, but that's actually just the color and font attributes that are then used by syntax highlighting) is based on :autocmd events (same goes for filetype plugins, so any C++-related settings you also wouldn't find in the split file, assuming you have :filetype plugin on in your ~/.vimrc). Without the nested attribute, the split file will be opened, but none of the usual actions will be run on them. Though nesting in general can be problematic, this is one of those cases where it is needed.
au BufRead,BufNewFile *.cpp nested exe "bel vsplit" fnameescape(expand("%:r").".h")
au BufRead,BufNewFile *.h nested exe "vsplit" fnameescape(expand("%:r").".cpp")
Unfortunately, this introduces another problem: The one autocmd will trigger the other one, and vice versa (up to a limit). You need to guard the actions so that a split is only done if the file isn't open yet. (This also improves on the usability in a general way, when you open a file with the other already open.) :help bufwinnr() checks whether the target buffer is already visible in a window:
au BufRead,BufNewFile *.cpp nested if bufwinnr("^" . expand("%:r").".h$") == -1 | exe "bel vsplit" fnameescape(expand("%:r").".h") | endif
au BufRead,BufNewFile *.h nested if bufwinnr("^" . expand("%:r").".cpp$") == -1 | exe "vsplit" fnameescape(expand("%:r").".cpp") | endif