The short answer to that question is a resounding YES. However, it is extremely important to know the reasons that something is a good idea, especially in regard to a health matter.
Too much time outdoors without proper eye protection is risky for adults & children alike. Even on cloudy days, UVA and UVB rays make it down to ground level and can reach our vulnerable eyes. Too much UVB exposure can lead to photokeratitis (“sunburn of the eye” or snow-blindness), pinguecula (benign growths in the eye), and pterygium (another type of non-cancerous growth in the eye), and too much UVA exposure can lead to conditions like cataracts and macular degeneration.
Depending on where you are outdoors, and what the conditions are, your level of exposure will be higher or lower (with snow, perhaps somewhat surprisingly, being the most dangerous as it reflects large amounts of UV rays which otherwise might’ve just hit the ground back into your eyes.
Since the eye’s lens cannot repair itself, damage to the eye accumulates over time. And, because children tend to spend more time outside (and unprotected), when compared to adults, as much as 80% of lifetime damage from UV rays can be accumulated by the age of 18!
The lenses of children’s eyes are less developed than those of adults, and consequently, they are less effective at stopping UV rays. Children also tend to look up more than adults, giving more opportunity for higher levels of UV rays to enter their eyes, and they are less likely to notice if their eyes are becoming sunburnt.
Acquiring effective eye protection for your kids, and educating them on why they should wear it, is not a particularly costly or time-intensive endeavor, and it can have a huge impact, especially later in life.