Winters aren't "bad" by weather standards. There's very little precipitation and the temperature at its coldest drops to right around 0C/32F, but usually the HIGHS are ~7C-12C/45F-54F and the lows are 3C-7C/38F-45F. So alright with a warm jacket. However...
It's a walking city and so you'll feel the climate more because you won't be getting into a warm car and then driving to wherever you're going. Waiting for buses will kind of suck and then you'll get on a crowded subte and think that you're going to melt with all of the layers you're wearing and all of the other sweating bodies all around you.
ALSO...
The northern hemisphere has stocked winter with plenty of holidays. Thanksgiving, Christmas, Chanukah (spelling is up to you), Kwanzaa (if you like holidays from the 1960s), New Year's, and even Valentine's Day are all "winter" holidays more or less.
Here they have their Independence Day (9th of July) that goes almost completely ignored other than no one works on that day. And then FRIEND'S DAY (20th of July) which is HUGE, but you won't have made any life-long friends in your first 2 weeks in the country, so that will be a non-event for you.
In summary, the winter is just kind of depressing. You won't notice that you're feeling down, but it's there. The weather's not too bad, everything will be new to you, you'll be like Curious George snooping around in new shops, but there will be a slightly leaden cloud that you hopefully won't be fully aware of because you'll be so focused on getting settled and meeting people. And fortunately this year Argentina will be hosting the Copa America (South American Soccer Championship) and you will be able to experience watching that in some crowded bars...
...but then that will end. And you'll be a bit depressed. You won't know why, but it's there.
Then September will hit and with it comes spring.
The days will be getting longer, the weather will be getting warmer, bulky clothes will come off, fit bodies will be everywhere, you'll spend time in the park, and you'll feel excited about the Spring/Summer seasons ahead and possible trips to the beach to plan, the Rugby World Cup will start up (though the games will be in the middle of the night because it's in New Zealand), you tag along with a group going to a "fútbol" match and you'll pass Parque Las Heras on a bus and you'll see guys & girls in bathing suits "tomando-ing sol" and you'll think- "Jesus, winter sucks in Buenos Aires! But the spring is AWESOME!
That's winter in Buenos Aires.
Thankfully it only lasts 3 months (or less). In other places in the world it can be nearly half the year.