Hi Faisalk,
Yes, the wind does play a role and No, flying in windy conditions does not mean that it will crash. The effect of the wind increases if it is a high wing trainer with dihedral. There is no specific "safe" wind speed for a particular model to be flown but larger low wingers without dihedral tend to handle wind better than smaller high wingers with dihedral. I have seen accomplished pilots fly with ease in stormy conditions while novices struggling with 15kmph winds.
It all depends on your confidence level and what you can handle.
Just remember that when learning, always take off and land into the head wind. Try and avoid low flights in a crosswind in the beginning. Cross winds tend to buffet high wingers around. If you are too low, your scope for recovery reduces.
Also remember another thing. A stiff headwind drastically reduces the ground speed of the aircraft. So make sure you have enough power or/and a steeper glide slope when making the approach into the wind. Else, you might struggle to reach the runway if you try to glide it in like on a non windy day.
Cheers
Lavneet
New Delhi