Kriff, Ahsoka hated snow. It chilled her to the bone and made her feel damp and wet and no matter how much she bundled up she never felt warm.
As for why she was out in it, at first it had been simply so that she could clear her head. Meditation wasn't working, the apartment was feeling too big again.
And then providence or the Force had led her in this direction, where she'd sensed Anakin.
She made no attempt to quiet her footsteps in the snow.