I have a 2011 Justa convertible and I foolishly removed my winter tires early and needless to say there just had to be one more spring snow storm in March with my car shodded with its summer tires. I got stuck on a slight incline. In the flat just before the incline the TCS was going off constantly and I could move but only at a snail pace. On the incline I couldn't move at all with or without the TCS on. I rolled back down the slope in reverse into a snow covered parking lot of a former Walmart store . I found even on the flat ground in the parking lot, with about 3 inches of unplowed snow, I could move going backwards in reverse but not forwards. TCS was on. Was that simply a function of the tread pattern of the tire working better in reverse on the snow or is there no TCS functioning when you are in reverse?

 

When you are driving up an incline....there is a weight shift to the rear...so you loose traction...
Not sure of the question...but it's an old trick to back up a hill with a front wheel drive car in a low traction situation.

 

I get that for the incline but I still couldnt move forwards or at least I moved a lot better in reverse on the flat in the snow covered carpark which got me thinking maybe the TCS kicks in only going forwards.

Maybe I'll have to try this again next season!!

 

With summer tires , sometimes just the crown of a road, or the grading of a parking lot to make it drain is enough!! Lol...guess since you were also mushing down the snow with the fronts going backwards it helped...but driving on hockey pucks suck...lol..
Been there...done that with with my snows when I swapped then a couple days too early.
Did you try to disable the traction control....on my gen1 I had a switch...and had it modified for "track mode too...kinda had to flip it when you had deeper snow....even on a driveway with snows on.

 

I did turn off the TCS and found that with the TCS on, if I could move at all going forwards it was at a snail pace ( I had a city bus overtake me at an intersection and make a turn in front of me!!) , otherwise with it off it was nothing at all or an occasional lurch and then get stuck. In reverse with it on or off I just did better than forwards!

 

I would say that it's because reverse is the lowest gear, and the car was applying too much torque in forward even with traction control.