Gas grill: Is the nozzle from the gas tank that goes to the grill suppose to turn ice cold?

If it is the gas fitting that connects the LP tank to the grill that is frosting up, it could be that it is leaking. This happened to me. Try opening the gas valve on the tank but leave the grill off. If it frosts up and you smell gas try tightening the connector. Be sure to wear gloves and turn the gas valve back off first because the connector may be very cold! If this does not work the gasket may be bad. You should be able to get a new gasket at the same place you purchase your LP. Another way to see if you have a leak at the regulator and connector is to open the gas valve on the tank, leave the grill off, take a little water with lots of dish soap in it and apply it generously to the regulator and connector. A leak will blow bubbles. Then try tightening up the connection that is leaking. Hope this helps. Good Luck!

When compressed gasses (or liquified petroleum gas in your case) are allowed to expand and release pressure they cool off.

Your freezer works on the same principle - there's an electric motor to compress the gas in the refrigerant lines (you can feel the heat given off the coils, typically on the back or bottom of the unit). The compressed gas is allowed to expand, cooling the freezer compartment.

It's normal. You were probably experiencing some high humidity outside at the same time... that accounts for the frozen condensation on the connectors. It's not dangerous.