No, Light does not inflict blindness.
Spells only do what they say they do. Since the description for Light doesn't say it can inflict blindness, it can't inflict blindness. Rules as written this simply isn't an option, no matter how it is used.
There's other concerns here as well.
With the question answered, there's a couple of other things you mentioned that should be addressed.
First things first, Light can't be cast from range. It's a touch spell, so the person casting it would have had to be touching the snake's nose while casting Light. They would not make a ranged attack roll to do this.
Next, Light specifically states what must be done when casting it on a hostile enemy. Rather than the caster making a spell attack against the creature's AC, the defender must make a Dexterity saving throw against the caster's spell DC.
Third, Light can't be cast on a living body part; the spell states that it makes an object glow with light. Now, one could argue that "a person's nose" is an "object", but the Basic Rules state that an "object" is "a discrete, inanimate item". As a result, someone's nose would not count, and the player should not have been able to cast it on the snake's nose.
But it was clever, and I want to reward that as DM.
but it's a smart idea so I think I should give him some chance to do something like that with it if he can, at least sometimes.
Of course, you're the DM. If it was a particularly clever use of the spell and you wanted to reward that, then by all means, do so. If my players were in a very dark cavern and the snake's eyes had fully adjusted to the darkness and my players suddenly shined something with magical light directly into it's eyes, I'd probably rule the same thing: a turn or two of disadvantage on the snake's attack rolls, as a small reward for smart thinking and interesting roleplay.
However, there's some serious combat balance concerns here, and I'd definitely not allow it multiple times. If you allow this all the time, your players now have unlimited chances to inflict an hour of blindness on an enemy at no cost to them except the caster's action; doesn't even use a spell slot. You would essentially be giving a level 2 player infinite casts of a much stronger version of a 2nd level spell!