05 E320 CDI

When the engine is cold (and in the cold ambient temps here in NH this time of year), the car has a very noticeable vibration at idle when the transmission is in Drive. None at all in Park, and only slightly in Reverse. When the engine reaches operating temp the vibration disappears.

I've inspected the engine mounts from above and they look fine, though I believe they are original. Anything else I should be looking for? Should I have the engine and trans mounts replaced at this mileage anyway?

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05 E320 CDI - 185K miles
82 300D - 200K miles (sold)