Ok, those were the results I got as well, before steps listed below.
I managed to fix things on my main machine (Ubuntu MATE 16.04.2, LibreOffice 5.3.1.2) , thanks to a tip in this post at StackOverflow.
- Go to fontconverter and upload your wingding.ttf.
- You get back a zip file, extract the converted wingding.ttf. from it (original-wingding.ttf is in the zip file too, as a backup).
- Replace wingding.ttf in your Windows fonts directory with the new, converted one.
- Do the same with webdings.ttf.
- Update font cache (fc-cache -fv;sudo fc-cache -fv).
- Test in LibreOffice.
For some reason the converted fonts didn’t fix things on my laptop, which has Linux Mint (16.04.2 LTS based) and the same LibreOffice version. I got webdings working but not wingdings. Will have to take a fresh look in the morning.