I can't remember whether you said or not (before) whether the knocking
was in frequency with the cam or with the crank.  There is such a
thing as piston slap although I have no direct experience of it
myself.

You need to try to find where the sound is coming from really and only
someone experienced with the different failure sounds could probably
tell you that.

I had a car once that was tapping and it turned out to be shapnel
imbedded in the top of the piston.  My dad's Saab had the little ends
go.  My GM sounded like the cam was on the way out but turned out to
be water pump bearings.

Your car uses HYDRAULIC valve lifters. These are thin devices that are
rougly the size of a small stack of nickels. The lifters are prone to
getting an internal build up that restricts the free flow of oil, OR the oil
flows properly but the spring inside gets stuck in such a manner as the
lifter is slightly collapsed when cold.

1.) There is very little you can do for this beyond adding a detergent
product (automatic tyransmission fluid works here) to clean the contaminants
out and hopefully regain full operation of the lifters. There are a variety
of detergent-products you can add, automatic transmission fluid is what we
used in the old days before the specialty products that may or may not work
better.

2.) Before we got hydraulic lifters, valve noise was common. A slight tap
from the lifters (where the rocker arm contacts the top of the valve) is not
a problem. It is an annoyance, but it is not a problem.

3.) Cold weather plays into this trouble because the oil gets thick when it
is cold, and thick oil does not flow through the very small orifices inside
the lifters, causing them to tap until the oil gets warm. One of the
available remedies is to use a lighter weight motor oil in winter. If you
are using 10w40 now, try switching to 5w30 for winter use, then back to
10w40 for summer.

Hydraulic lifters expand to fill the space between the valve stem and the
rocker arm so there is no noise coming from the valve train. When the cam
lobe rises, the rocker arm presses against the valve stem, pushing the valve
open. Because the valve has a very strong spring, some of the oil inside the
lifter will get pushed out as the rocker arm pushes the valve. When the cam
lobe falls, the rocker arm releases the valve which is closed due to the
very strong spring mentioned earlier. There is a small spring inside the
lifter to cause it to expand again to fill the gap that forms between the
rocker arm and the valve stem. When the lifter expands, oil flows in and the
valve train sits and waits for the cam to roll around again and start the
whole process over.

The problem you are noticing is that the lifter is not fully expanding when
it is cold, and the tap you hear is the result of the small gap between the
rocker arm and the valve stem. The cause of not expanding can be dirt/sludge
inside the lifter, blocked passages impeding the flow of oil, or thick oil
that is slow to run through the passages. Of course, a combination of all of
these is possible as well. One other possibility is a broken spring inside
of the lifter, but this would make a sound that remains after the engine
gets warm.

I said earlier that the lifter goes between the rocker arm and the valve
stem, but this is not always the case. The lifter can go between the cam
lobe and the rocker arm, and on a push-rod motor it will almost always rest
on the cam lobe, with the push rod fitting between the top of the lifter and
the rocker arm (the configuration of a push rod motor is not really germain
to this discussion since your BMW does not use that design). The point
being, the physical location of the lifter is not important, the job it does
is what I wanted to describe. Once you understand what a lifter does,
finding it is easy. The job of the lifter is to fill the small gap that
exists between the rocker arm and the valve stem. There are engine designs
where the cam makes direct contact with the valve stem through the lifter,
in this instance the lifter will need some form of device to hold it in
place. (Your BMW does not use this design either ... )

Bottom line,
You worry too much.