The time of year you travel to Antarctica does make a difference. However, deciding what time is "best" depends on what you are personally desiring to get out of your adventure. Particular wildlife sightings - mating season - new penguin hatchlings - specific weather - icescapes - mud - penguin poo smell at its worst/best...?
November: The month of November (late Austral spring and early Austral summer) undoubtedly offers the most adventurous time to visit the Peninsula. This is the time to see Antarctica in its most undisturbed form. Temperatures tend to be colder and polar ice is still breaking up, restricting access to some areas. However, the cold temperatures also offer the most impressive icescapes, pristine snow and breathtaking scenery. Whales are typically not as plentiful as later in the season, though you can still commonly see them. Seals and penguins are quite active, and it is a great time to observe the penguins squabbling over pebbles for their nests. By the end of November you'll see lots of nests with eggs!
December to Early February: December and January are the months with the most sunlight (up to 20 hours a day), and daily temperatures are at their warmest. In January, temperatures at the Peninsula average 34 Fahrenheit. Penguins begin hatching and wildlife, especially penguin chicks, is most plentiful during this time of year.
Mid-February and March: Late summer in Antarctica, February and early March, is the best time to spot whales. However, you are likely to see fewer penguins as many will have already returned out to sea. By March, the chicks are quite large, and they start to fledge. Weather wise, temperatures are beginning to drop as the season starts to change. Daily highs average roughly 29 Fahrenheit on the Peninsula. There tend to be fewer vessels operating at this time, which means you won't have to compete with other ships for landings. This time of year you are also likely to have better access to areas further south as polar ice melts. You will rarely walk on snow during this time; expect rocky and muddy landings.