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Zurich HB is Zurich’s main station where your train to Bern - Zermatt will depart and also the closest located to your hotel anyway, so yes. You might want to consider leaving your skis/snowboards at the luggage service there instead of also hauling them to your hotel.
There is no additional cost for personal luggage you can carry yourself in any public transportation in Switzerland.
The only downside of Saver Day Passes are the very limited refund conditions in case of a change of plans (medical reasons with provided doctor’s certificate only), while a p2p ticket is fully refundable no questions asked until the day before its validity date.