Hello. I recently changes the shut off valves to the outside sillcocks on my house in CT. There is about 3 feet of pipe between the shut off valve and the rim joist where the pipe exits to outside. I insulated this pipe to help prevent freezing. Now, I'm thinking this may be wrong. The basement is about 40 degrees at the coldest in the winter. Does the insulation help or hurt my cause here? Thanks

i think you are asking if the shut off is within 3 feet of the rim joist, is that too close?
if it faces north, you are close but should be fine.
if it faces south it is OK..

The 3' of pipe should be empty, right ? Insulation will neither help nor hurt if that's the case.

The pipe may hold some water after shut off. The outside sillcock is left open and covered with a hood. What I'm concerned about is the pipe better off uninsulated and "feeling" basement temp of around 40 or be insulated and maybe picking up colder temp from outside?

Pipes are damaged when water freezing expands and create pressure. The insulation does NOTHING to change the temperature of the water in the pipe so it is irrelevant. IF the water at the hose valve freezes and compresses the water between it and the shut off valve, that could cause damage, which is why shutting off the valve is usually not enough. You have to drain the water out of the pipe using the drain port on the shutoff valve, assuming it is the correct valve and has the drain.