Bailar is just a verb..... the noun for it would be BAILE..... "would you grant me this dance?" -- me podria conceder este baile??
Yo estoy frio........... isn't totally incorrect, although I don't know what exactly you're trying to say. When you use the verb "estar" it rather refers to a particular condition in a particular moment, so if I say "yo estoy frio" it rather means that your body is cold...... as in your arms, legs, face, etc. If you touch them and feel they're cold, you'd probably want to specify that your body is cold in that moment. If you want to say that you're cold in general (because that's what the weather is like) then you'd say YO TENGO FRIO.......