No, you do not need to present the same credit card that was used for payment for check-in purposes. However, you will need to present a credit or debit card for any incidental expenses that may be incurred such as parking or room service. You will need to pay for such incidental expenses at the time of check-out.
If you have any remaining lodging balance due at check-in, you are free to pay the remaining balance with a card different to the one used for the original booking with SnowPak.