I agree with the majority of posters who have recommended becoming familiar with the intricacies of the Mustang and the differences between a solid axle RWD and your AWD Forrester.
Also, keep in mind that they haven't yet repealed the laws of physics. If your Mustang can spin warm tires on a dry pavement in 100 degree temperature, it's going to be MUCH easier to spin them (reduce traction) on a cold, wet pavement.
My GT came equipped with the Pirelli P235/50/18 Zero Nero All Season tires. I have punched it a few times and easily spun the tires on dry pavement from a 30mph roll. At the same time, driving conservatively, I haven't noticed any lack of control on wet pavement. I don't agree that the issue is based entirely on the tires. I think it may be partially that, but probably more likely the fact that you're not used to the power under the hood that's being transferred to those tires. I'm sure there are better tires out there, but so far I have no complaints with the Pirellis.
Give it a little time for you and the Mustang to get to know each other a little better. And stay safe.
2012 5.0 GT - 6MT82 - Sterling Gray - Premium Sports Interior - Comfort Package - 18" Polished Aluminum Wheels