I installed Steam through Winetricks on Ubuntu, and I can't take any screenshots. I can't get the Steam overlay to come up either.
I've checked that the overlay is enabled in multiple places.
There is a bug with Steam under Wine, where the overlay causes some games to crash.
To prevent this, Winetricks installs Steam with one library override:
Which, naturally, disables the Steam overlay, and the in-game functions it provides, such as screenshotting.
To change this, open
winecfg in the proper wineprefix (for me, Winetricks made it
~/.local/share/wineprefixes/steam, so I used
WINEPREFIX=~/.local/share/wineprefixes/steam winecfg), and change it. I set it to Native then Builtin, and so far it seems to be working fine...
Unless you must have the overlay, I would disable this again when you're done taking your screenshots to prevent it from messing anything else up.