Is it ok to cover a thermostat with a picture?

no the thermostat will not work

No. The thermostat needs proper air flow to function properly.

Thermostats read the ambient temperature of the air in order to regulate room temperature. Covering the thermostat will restrict air circulation and possibly damage the thermostat by causing it to overheat.

I have covered fire alarms with clay or metal sconce covers that have cutouts on the front, open back, top and bottom. This allows air circulation and I believe it would not prevent the thermostat from reading the air. https://www.amazon.com/SW-Ceramic-Kachina-design-Terracotta/dp/B073SJBS2J/ref=sr_1_fkmr0_1?ie=UTF8&qid=1522168140&sr=8-1-fkmr0&keywords=ceramic+wall+sconce+with+open+back

I have been told that as long as there is air flow and you remember to dust the actual thermostat (carefully), placing a picture over a thermostat is okay. It may stick out at an awkward angle, however.

Not a good idea. The thermostat senses how cool or warm a room is and heats the room accordingly. If it's covered, it thinks it's warmenogh and won't trigger the furnace to turn on.

No, ma’am. Paint it with markers; or build a feature wall with pictures, mirrors, and tree branches around it and it will not attract attention; or paint the cover the same color as your wall. You could have it moved more out of sight, but that could be expensive, not as efficient, and would leave an area you have to repaint. Best wishes ☺️

don't know if that is wise but why not get a cool frame make it art

Yes

I put a picture frame around a light sconce and it looks great.