As a general rule, US rental car companies do not provide Winter tires as standard in any locations, and in most locations they are also not available even as options.
Many vehicles will be fitted with "M&S" (Mud and Snow") tires which are a mid-way between a standard tire and winter tires.
There is no legal requirement for vehicles to have winter tires, although obviously they can help from a safety perspective depending on the conditions.
As far as whether you can cancel or not, this will depend entirely on the conditions of your booking. Most car rentals in the US (especially with the major rental car companies) can be cancelled at least up until the pickup time with no fee. If your booking is one of these them obviously, yes, you can cancel now without any impact.
If you have a pre-paid rental then there will likely be a fee to cancel, although the exact fee will depend on factors like the company involved, where and when the vehicle was rented, and how long before pickup you are canceling.
The only way to confirm if there is a fee to cancel, and if so how much, is to check your reservation details and/or call the company involved and ask.
If they state there is a fee then you can certainly request they waive the fee based on the conditions, and in particular your concern the the vehicle doesn't have tires suitable for the conditions - but as winter tires are not a legal requirement any concessions granted would be at the discretion of the rental company.
If you do decide you continue with the rental you may want to familiarize yourself with how to check if a car has "Mud and Snow" (M&S) tires, which are standard on many vehicles now days. If the company is one that lets you pick your own vehicle, then you will be able to look for one that has these tires. If the company is one that assigns you a car, and the car you are assigned doesn't have M&S tires on it, you can always ask for them to swap you to a difference vehicle (of the same class!) that does and they will likely agree.