Turn off wine debugging
WINEDEBUG is an environment variable that is set for only for the invocation of wine.
What you need to do is make the environment variable permanent, which you can do in your ~/.bashrc.
Open it in your favourite editor and add to the bottom:
export WINEDEBUG=-all
The next new Terminal you open will trigger that setting and wine ./program.exe should inherit it.
Since .bashrc is just a series of shell commands that are run when a Terminal is started, you can just type the same thing into a Terminal as well; but then it will be lost when you close that Terminal.