I wouldn't use *crapahuter* which for me evokes too much militar activities like an assault course or a forced march.

As already stated:

- *patauger* implies there is some water so might work or not depending of the snow quality.

- *chez soi* is for third person (e.g. *chacun chez soi*.) Here you are talking about your own home, so *chez moi*.

I would remove the pronoun *en* from your sentence as it has no antecedent.

Here is what I would use if the snow is usually melting:

> J'ai des frissons rien qu'à l'idée de devoir patauger dans tant de neige jusqu'à chez moi chaque jour.

and if the snow usually stays frozen:

> J'ai des frissons rien qu'à l'idée de devoir [me traîner]/[progresser] péniblement dans tant de neige jusqu'à chez moi chaque jour.