I have this annoying noise from my blower motor when it's very cold outside, the noise disappears when blower blows at higher speed.

My problem is caused by a warped squirrel cage on the blower, there isn't much clearance between the squirrel cage and the housing, when it's cold the cage warps further and scratches the plastic housing, this is where the noise from, at higher speed, the cage straightens itself due to centrifugal force therefore noise disappears. In your case, the motor is new, it may be mounted slight off the center or the worst case, the squirrel cage is damaged during the installation.

The squirrel part has to be ordered with blower motor which is a $250+ part, it hasn't bothered me enough to waste 150$+for the motor that I don't actually need.

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99 BMW 540i 6-speed 110K Km
03 SAAB 9-5 wagon 80K Km
92 400E (Sold) 245K km
Still missing the days with the Benz, it kept me busy.