Can Varithena be used for spider veins on the face/around the eyes?

No. Varithena is a form of foam sclerotherapy and should not be used around the eyes or face for a variety of potentially serious reasons for which i recommend Veingogh for facial veins (see below).
While it is a 1% polidocanol solution and is highly effective for treating difficult and much larger varicosities in the legs, it is excessively potent for the face and could even skin necrosis if injected outside the vein. Much lower concentration of physician prepared foam sclerotherapy can be used for spider veins on the legs, but the foam can cause vasospasm or even thrombosis of the retinal artery which has a very rare but permanent risk of blindness. Do not do foam sclerotherapy in these very delicate areas please.
Tiny doses of liquid (non-foam) sclerotherapy have been considered, but why assume the risks? Instead, I recommend Veingogh which used a tiny needle to deliver variable brief pulses of heat and no permanent scarring, despite some minimal social downtime.