Yes, dipping your face in ice water has many positive effects and is even acknowledged by dermatologists! Just like ice baths or cryotherapy, the cold helps energize your skin and your mind. Glamour, a known beauty article that has certified dermatologists verify their findings, states, "Firms the skin, tightens pores and tones the skin, leaving a fresh and smooth complexion." Alexandra Bowels, board-certified dermatologist, continues to state, "Stimulates lymphatic flowpromoting skin health." Not only does it promote healthy skin, but it also releases endorphins that promote a decrease in stress. Dr. Bowels does make it clear that while these are all positive effects, it's a short-term "Pick me up"
Another reliable source, the National Library of Medicine, conducted a few studies of the health benefits of ice facials. In summary, the studies suggested that it can be an effective treatment for "Inflammation, stress regulation." They also agree that there needs to be moderation as well as maintaining a healthy lifestyle, explaining that other factors are included in seeing positive results.
In conclusion, there is scientific evidence as well as certified dermatologists who state positive effects in ice facials, but also express the importance of balancing with other healthy lifestyle choices.
https://pmc.ncbi.nlm.nih.gov/articles/PMC9518606/
https://www.glamour.com/story/ice-water-facial