Learn English – *In* or *On* Contacts

I believe this to be a case of inversion of an accepted alternate form. In other words: many times questions are formed by inversions of statements and this is an inversion.

What color[ed] eyes did she have?

Inverts (more or less):

She had blue colored eyes.

There is a tendency in spoken language to swallow the -ed at the end of a word. And, this tends to find its way into the written form. Hence color vs. colored.

When you consider this a truncation of the -ed, you will see that a preposition is no longer necessary because it is an adjective being used as an adverb.

Consider another case:

What size shoes do you wear?
I wear size 7 shoes.

Most people don't say sized 7 shoes. So, this form stays intact in the question. And, you'd never say size 7 of shoes. So, you would be unlikely to use the form:

What size of shoes do you wear?

It just sounds awkward (at least to a speaker of AmE).

As, FumbleFingers rightly states in comments above: much of this is related to your "inner grammarian".

You can rather easily argue that to belongs to its own part of speech. The only evidence you need is that it does not fit into any of the major part of speech categories. You will just construct grammatical tests showing that it is not a noun, not a verb, not a preposition, etc. Following examples suggest that to is not a verb or noun, and that other prepositions cannot precede verbs in their base form (respectively).

*Nobody shall to.
*The to is ready.
*It is hard to see with run.

Of course, you can go on with this type of argument with pretty much any high frequency word until you have so many parts of speech that the concept is no longer useful. Of possible interest is Croft's discussion of Word Classes in Radical Construction Grammar.