Only carrier that has listed specific dates is Verizon Wireless.
"They have listed their Apple Watch Series 3 offer for purchases from Verizon Wireless or an authorized Verizon Wireless retailer between 9/15/17 - 12/31/17 and we'll waive your activation fee and line access charge for the first 3 months."
Every carrier might vary, but I would assume the trial is not something that can be used as a service whenever you want. It's likely offered for a limited time unless, that Carrier makes an exception.
Dave and Relentless are correct. You need to activate the LTE now, if you want to take advantage of the free trial offer (provided you are with Verizon). As to the other carriers, nobody knows for sure when they will stop the offer.