PA28 student pilot reported failure to compensate for crosswind resulted in runway excursion and nose gear failure.

Narrative

I was on a student solo training mission. The training involved pilotage to a nearby airstrip within a 10-statute mile distance with return to ZZZ; the airport of my departure. Taking off winds were 340 at 6kt and within my endorsed limitations. Arriving back to ZZZ I checked AWOS; and winds were coming from 210 at 6kt. I attempted a landing on runway XX. While coming in for XX I noticed the wind had changed and I had a strong crosswind. I chose to go around on runway XX and went back into the pattern to recheck the weather. The wind was now coming at 6 knots from 340 from what I remember; so I chose runway XY for approach. I was lined up on center line all the way on approach until I was in ground affect. While in ground affect a large gust pushed me left of centerline. On touchdown I attempted to correct for the crosswind with ailerons into the wind; but it proved to be outside of my skill level. I was pushed off the left side of runway XY and due to soft/muddy ground the front landing gear collapsed; and the prop hit the ground. I was able to shut down the aircraft and exit unharmed.