L Dutch's Answer does a really good job of explaining how Kepler's law of planetary motion works, but it is missing some pretty important details about axial tilt.
While the eccentricity of your orbit will make some seasons longer than others it will not affect your whole planet the same because while your Northern Winter may be longer, your Southern hemisphere could have a shortened winter and a longer Summer; so, this fails to get the desired effect on a whole Earth-like planet without messing with some other variables as well.
Technically, you could move the orbit enough so that you get the same season on both hemispheres of a tilted world, but this would cause compounding issues that would make one hemisphere uninhabitable. If your planet were to have an Earth-like tilt you'd have to make the orbit especially escentric to create an Earth-like "short summer" across the whole globe which would cause one of your hemispheres to experience twice the seasonal variance that you see on Earth. So, while Earth's Temperate zone typically varies by about 40°C, a similar would with such an orbit would have a variance of 40°C in one hemisphere, and 80°C in the other. While 80°C may not sound like too much variance for life to adapt to, it is certainly very bad for macro-organisms. Your extreme temperature gradients and maximum temperatures reaching 60°C in one hemisphere will not just cause deadly heat, but massive storm systems including but not limited to hypercanes with wind speeds exceeding 800 kilometres per hour followed shortly by a long sub-arctic winter. Tardigrades might get along just fine here, but macroscopic organisms generally take issue with silly things like freezing their body fluids, folding their proteins, and being ripped limb from limb.
For a more consistent "long winter" there are a few solutions that may yield the desired result:
One solution is to give your planet very little or no axial tilt with an eccentric orbit. This would mean that your planet would not get seasons at all the way the Earth does, but only get seasons based on its physical distance from the sun.
Another way to solve your problem could just be to make your planet colder: either by reducing its greenhouse gasses or by moving it closer to the outer limit of the Goldilocks Zone.
While this second solution will not actually make the coldest time of year any longer than the warmest time of year, it would give you a longer winter from a biological point of view. On a colder planet, plants and animals may need to be dormant for longer portions of the year waiting between when things are frozen and when they thaw out enough for macroscopic life to thrive effectively giving you a longer winter.
This second solution may be a better option if you want your civilization to still be able to rely on solar calendars to measure years since they sun always follows the same track in the sky on an untilted world.