Translation:Your soles are cold, don't you have socks?
Yes, you can use singular with probably any of those paired body parts. Otherwise "talpad" is singular, "talpaid" is plural.
In the Beta answer your translation is wrong. In the negative you cannot use "you've" to mean Do you not have.
The "full" sentence is:
"Hideg a talpad, neked nincs zoknid." Right? The dative possessor "you" is just omited, since van/nincs + possession is enough?