Would laser resurfacing help with facial hair and or small veins on the face?

Thank you for your question. I suggest that you move forward and consult with your board certified facial plastic surgeon.
Best wishes,

Hello, thanks for your question.
Laser resurfacing, also known by its procedure name Pixel Fractional Laser, is great for improving skin texture, sun damage, pigmentation, acne scarring, scarring, skin rejuvenation, sun spots, skin tightening and wrinkles. 
However, when it comes to treating facial hair and small veins, laser resurfacing will not help. IPL would see better results.
Intense Pulsed Light (IPL) is a gentle, safe and cost effective way to permanently reduce unwanted hair on most parts of the body. It's also effective in minimising unwanted skin spots, leading to overall rejuvenated skin as well as a reduction in hair.
Regardless which you choose, a doctors setting is the best for treatments like these. Thank you and wishing you all the very best.
Stay safe and well, Dr. Murray from Absolute Cosmetic Medicine

Laser resurfacing is excellent for fine lines and wrinkles. Typically either CO2 or Erbium devices are used. These wavelengths do not offer much benefit for unwanted vascularity (blood vessels) or unwanted hair. There are, however, specific devices for these as well- I would recommend consulting with a physician who uses lasers on a regular basis to explore your options.

Resurfacing lasers are typically used to treat fine lines and wrinkles, textural abnormalities, and scarring.  Removal of facial hair is typically performed with different types of laser, ones that targets cells in the hair follicle.  Likewise, small veins on the face are removed by lasers that target red blood cells inside the vessels to ablate them.  So, while lasers can certainly be used to accomplish both of the things you mentioned, it is not specifically a resurfacing laser that will accomplish the removal of hair or vessels.  Best wishes.

Laser resurfacing removes fine lines and wrinkles. You will need other kinds of laser treatments for veins and hair.
Our clinic specializes in vein erasure. For the small veins on the face, we use pulsed dye lasers (PDL), intense pulsed light (IPL) and/or Nd:YAG lasers. These can treat both telangiectasias (red spider veins) and recticular (blue) veins. As for the facial hair, it can be removed with IPL. It will probably take several sessions to remove all of the hair. Be sure to consult a board-certified dermatologist who specializes in vein and hair removal.