Sounds like a bad motor mount, if the RPM is stable. They tend to be most noticeable in the 2-3k RPM range, and the cold weather would harden the rubber, accentuating the issue when it's cold.
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1999 Ocean Blue Metallic Boxster - blueboxster.com
Sounds like a bad motor mount, if the RPM is stable. They tend to be most noticeable in the 2-3k RPM range, and the cold weather would harden the rubber, accentuating the issue when it's cold.
Can also check the tranny mounts -- because they essentially act as the other side of the engine mounts.