Is it warm or cold water better for washing face?

Either: There is no evidence that I am aware of that demonstrates either cold or got water being superior in terms of washing your face.

Not critical: Better is a relative term, so I am not sure how to answer it. Warm can open pores and cold can close them, so maybe start warm, finish with cool. Be cautious with too hot or too cold as extreme temperatures can cause damage to skin. As i assume you are addressing acne, use mild soaps and clean gently. Often over the counter benzoyl peroxide can be a good addition to skin care. Caution with make-up.