The sun spends more less time near the sun around the winter solstice than during the summer solstice. The sun may also be further away during that time because eclipses are more likely to be annular in summer than in winter. (but this is a small effect). It is not clear that Hyparchus could have noticed this as there are only about one central eclipse near Greece in a hundred years, so it is hard to get statistics. Ie, the sun goes through the sky faster in winter than in summer.
Note from the times, the sun seems to go fastest in the winter to spring, than in the fall to winter-- not by much. This suggests that the sun is going fastests just after Christmas. (It actually happened at around Jan 6, but they could not have measured that. That is also when the sun is largest in the sky. It's diameter is about 3% larger (in diameter) then than in mid-summer. Again this would have been impossible for them to measure.).
Note that we now demand that all seconds be the same (the same fraction of he siderial rotation of the earth around its axis). It used to be that noon was defined as the time when the sun was highest in the sky, and it was defined that there were always 12 hours of daylight and 12 of nighttime. Ie, hours and thus minutes and seconds were of different lengths day or night, and were of different lengths throughout the year. It was only when mechanical clocks became readily available that time was redefined so that seconds were equal.