Pipes start icing at 20ºF and below. Down to how many ºF do the foam sleeves protect the pipe? The foams I placed in my outdoor pipes had a 0.35" thick polyurethane foam surrounding them.
This is a picture of the sleeves I installed:
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There is a time aspect not just r-value. No matter what r-value something has it doesn't keep something warmer for an infinite amount of time. If there is no temperature coming from inside the pipe (pipes just laying there), then the pipes will very soon be the same temperature as outside.
What you are relying on is the temperature inside the housing to provide this section of pipe with warmer air. Which depends on the temperature inside and the amount of water flow through this section. Really no way to answer the question accurately because there are a ton of variables. You are going to get way more warm (inside) air dispersed on the pipe by keeping the water running than by putting a sleeve on it for example.