There certainly are weather effects. Right off, a team that builds its offense around the long ball (which is arguably the Phillies) is going to take a hit to offense in cold weather (cold air is denser, balls don't carry as far). If its really cold, it can affect pitchers' ability to grip the ball, which can hurt some pitchers more than others. As you said, these things impact both teams - but if your team is built in certain ways, it can be challenging.
As it happens, the Phils shouldn't have weather issues (apart from possible rain) early - they open in Texas, where it's forecast to be warm; then go to NYC, where the forecast is pretty balmy for early April (lows around 50ºF), then afternoon games at home vs the Reds. FIrst home night game is 4/10; I don't have a weather forecast for that far out (and it wouldn't be too reliable if I did!).