Art cold? To what extent can pronouns be dropped in English?

Solution 1:

Yes, this was ordinary colloquial English in Shakespeare's day, although you was rapidly passing thou. Here are three more instances from Lear:

Art of this house?
Art not asham’d to look upon this beard?
What, art mad?

There was also a contracted form in the indicative:

As th’art a man, Give me the cup. —Ham
Well said; th’art a good fellow —2HIV
Th’art a tall fellow; hold thee to that drink. —TS

An interesting fact (although only marginally relevant to your question) is that Elizabethan/Jacobean English was as likely to contract the pronoun as the verb be. Our it’s appears as ‘tis, our you’re appears as y’are, and our he’s appears as ’a’s—indeed, ’a is the ordinary unstressed form of he:“’a babbled o’ green fields”. (And as often as not, the apostrophes are missing in the printed texts, which can be disconcerting.)