Does sunlight warm an astronaut's face during a spacewalk?
Perhaps a little, but not much.
Most About 40% of the power in the Sun's spectrum is in visible wavelengths (not a coincidence, in several ways) so if the astronauts can see, then the Sun can see them too! There's no such thing as a one-way mirror.
Looking at the photos in the question, you can't see the astronauts' faces but instead see a fairly bright reflection. The visor is essentially an overgrown pair of mirror sunglasses, so reflective that only a small amount of light makes it through.
Exposed directly to sunlight in space with a solar constant of 1361 W/m^2, a 20x16 cm^2 face would receive 40 watts of heat, and that's a lot! It would only be a little less with a face plate transparent to all wavelengths on a suit, and a combination of air conditioned air would remove some of it and the extensive blood flow to the face would remove some, but it would probably feel a bit warm if the astronaut turned from facing space to facing the Sun.
However, assuming the faceplate reflected or absorbed much of the invisible infrared light, this would be less. As shown below, in space the ATM0 spectrum integrates to roughly 1350 W/m^2 but the part in the visible range is only about 530 Watts/m^2. So a 20x16 cm^2 face would only receive about 17 watts of heat induced by visible light.
Then, assuming the mirror attenuates say 80 or 90% of the light, then we'd be around 3.4 to 1.7 Watts, and that's probably well below the warming from the natural thermal infrared radiation that the face plate or anything will already radiation towards the astronaut's face.
So yes, there will be a non-zero amount of heating, but with the reflective visors the astronauts use, it will be small and not very noticeable.
Data from https://www.nrel.gov/grid/solar-resource/renewable-resource-data.html
More info here https://cdn.ymaws.com/www.nfrccommunity.org/resource/collection/D60BEDFE-E54A-462F-9FA2-59693434DAC0/ASTM_G197-08.pdf
Python plot with https://pastebin.com/T3dY016N