Can my customers see which hotels can be cancelled free of charge and up to what date before they book?

Yes, in most cases they can see that before they pay. A hotel booking API normally sends a cancellation policy along with each room rate, so your portal can show on the room itself whether the rate is refundable, whether there is a free cancellation window, and the date the window closes. Many portals also show the same wording again on the payment page and on the confirmation, so nobody can say they were not told.

How clear that wording looks does depend on the supplier behind the rate. Some suppliers send the deadline as a proper date the portal can read and display as a short label, while others send the policy as a block of text written by the hotel, which the portal has to show as it is. A few only return the full policy once the room is selected and priced, so the detail appears a step later rather than in the first list of results. Non refundable rates are almost always marked plainly, because suppliers treat that as essential information.

It is also worth knowing that free cancellation deadlines are usually set in the hotel's local time, not your customer's time, and that a rate which looks refundable can still carry a charge if the guest does not show up at all. Filtering a search so it only shows refundable rooms is possible with most suppliers, although rates that arrive without a readable deadline may be left out of that filter.

Before you go live, run a few searches on hotels you sell often and check that the cancellation wording appears where your customers will actually look, and that the same wording reaches them on the confirmation email.