Why jet stream is stronger in winter?
Jet streams are influenced by the horizontal temperature gradient between two air masses which creates what is called a "thermal wind component", which when supplemented by the actual wind movement, creates the local acceleration of wind running along the top of the frontal boundary into a jet (above 90kt), and which is always nestled into the warm air side, in the wedge of warm air just under the warm air tropopause. 

The strength of the jet is therefore influenced by the temperature difference between air masses.  In winter the airmass boundaries (in North America) tend to move south, and the temperature differentials increase compared to summer.  With the higher temperature differentials and higher horizontal temperature gradients, the stream velocities tend to be stronger and they reside farther south.

If you really want to understand aviation weather theory, the absolute best book for this is the Royal Canadian Air Force Weather Manual. Can't recommend it highly enough.