Turn over the chair and use a small scruber or tooth brush, and clean the caster with soap water or alcohol. This will remove dust and keep only hairs and threads that got tangled.
Remove the visible hairs using butter knife on the crevice of the caster on both sides. Tweezers are good to use.
Use nail clippers or a bottle opener. It will have pointed curve. Insert it into the fissure, Catch the hairs and pluck off the hairs. Keep revolving & rotating the caster strategically by other hand while doing this and this will help the tool to catch more hairs.
Then, cut a section of duct tape and then stick around the cover and pluck off. You can also cut a section of duct tape and fold it back around your razor knife so that it will be like a closed loop ready to stick, then insert it under the wheel cover and pluck off. Reason why Razor knife is because they are very thin. Don't use the razor knife to cut though.
Or.
If you unscrew the wheels off and take them outside, Use a lighter in small quick bursts to burn the hair but not melt the plastic. (This is probably bad advice but it is effective)