I've noticed something similar on my 2003 XLT since it turned cold this year... I get a whistle on slow, continuous acceleration that goes away as soon as I take my foot off the pedal. When I put my foot back on the gas it takes a minute or two but it will usually return.
I started typing "engine whist..." into Google and it auto-completed "engine whistles when cold," so I figure it must be a problem common to a lot of different vehicles. Some people think it is just cold air in the intake causing metal to expand at different rates until the engine warms up, some people think it is a weak alternator or belt, and one guy said he just lived with it until he got old enough that he couldn't hear it anymore. :grin:
My plan is to wait until Spring to see what it does then.