I have 2014 Audi A4 and recently I drove on 1 inch snow and on sleet. I noticed when I tried to brake gently, I felt like something is pushing me back for a sec or two. I didn't feel anything while driving on dry surface of road and braking. What could be the reason? Is it normal?By the way, I hear a slight brake squeak sound when I press the padel gently and I am not sure if it's related with it.
What you're describing sounds like the pulsing feedback that the ABS (antilock braking system) provides when it actuates on a slippery surfaces.
The best way that I can describe it is as a roughness or rumble in the brake pedal, usually it is accompanied by a matching (for lack of a better word) sound. There may also be a annunciator light in the instrument cluster that comes on when the ABS activates.
It is perfectly normal and serves as a warning that the car is on a slippery surface and that one or more of the wheels was getting less traction during braking. As you're probably suspecting by now, you don't feel it on a dry or even wet road because the system doesn't usually come on.