Why is cold air fast in an occluded front, but slow in an anti-cyclone?
I do not think that there is a general relation between the temperature of an airflow and its velocity in meteorology. 

There are several physical processes that need to be considered when thinking about the surface winds in occluding cyclones or fronts. A possible mechanism that I could think of explaining the stronger winds in the cold air compared to the warm air is the difference in vertical stability. The colder air is often characterized by steeper lapse rates (a stronger decrease in temperature with height). This leads to more exchange of momentum between the near-surface air layer and the so-called free troposphere air aloft. This exchange accelerates the surface winds compared to a situation where there is less exchange (as is the case for the warm air in an occluding front).

In a (wintertime) anti-cyclone, the cold air establishes itself mainly close to the surface due to radiative cooling. This leads to a very stable vertical profile, meaning that there is not much exchange of momentum between the near-surface layer and the air aloft. In such a situation, one can say that the surface layer is decoupled from the free troposphere. When a front moves in, it will simply move over the cold layer at the surface without disturbing it too much initially. The cold air indeed moves only slowly in this case.

Hope this explains at least a part of your question.