I agree that toothpicks (bare wood) will be fine at the lower temperatures used for curing polymer clay (and well up near or over 500F). In fact, all natural materials are fine to bake in/on polymer clay *as long as* they contain no moisture (which could turn to steam during heating creating bubbled clay, etc)--wood stone, metal, glass, ceramic, etc.
The paint you have on the toothpicks might be a problem though, or it might not.
If you used acrylic paint, that's a type of plastic and the temperatures at which plastics are affected by heat vary a lot but generally in the 200-300F range. So acrylic paint could darken a bit for example, or even bubble if it's not thoroughly dry first.
If you used a dye, ink, or watercolor, higher-temps can probably be tolerated.
If you used enamel paint, not sure what the various temp tolerances would be.
This is all presuming that the temp reaching the paint and the clay in particular is actually what you think it is, which is not always true. You can tell that temp by using a cheapie oven thermometer next to the clay (in a preheated oven), or by "protecting" the clay or other things from darkening/etc in several ways while in the oven.**
If you don't want to bake the painted toothpicks and clay together, you can pull them out of the raw clay and bake the clay then reinsert the toothpicks. The clay may have tightened up inside the holes just a tad during heating so could be hard to get back in all the way unless you kind of wiggled each toothpick before removing to enlarge the hole slightly. Since the shanks inside the clay would be long you they'd probably be held in well just with pressure, or you could apply a bit of glue before inserting (permanent white craft glue, or most other glues).
You can read more about using "inlays" into polymer clay and various materials that can be baked with the clay, etc, on these pages of my polymer clay encyclopedia if you're interested:
http://glassattic.com/polymer/covering.htm (most materials and items listed on this page are fine for baking with polymer clay)
http://glassattic.com/polymer/mosaics_inlay.htm (click especially on "Inlays")
** https://answersrip.com/question/index?qid=20111224000037AAQSEfC (see the first link in my answer to this previous question especially)