Where did you have your small reception?

If you are just wanting to go with your guests to a restaurant to eat afterwards (ie, not decorate, have entertainment, etc.), I would suggest not informing the restaurant that it is wedding related in any way. I would just call and say you would like to make a reservation for 25 people for dinner. The moment you say it is wedding related, suddenly they want to have you rent out a private room, order off a limited menu, charge you more per person, set minimum person/dollar amounts, etc. If you are simply going there to eat a meal, there is no reason for them to need to know where you are coming from prior to that.

We are doing outdoor dining at a restaurant that has a heated patio

My parents backyard! Borrowed tailgaiting tents from a friend and had it on their stone back patio. Rented a toilet trailer. It was lovely and catered and perfect.

^left out that we had space heaters and sided the tents. Everyone was warm enough for food and drinks

We had an outside backyard reception in mid October and rented a tent and a patio heater. It dropped to 40° but the heater worked well. We also provided blankets (thanks to the in-laws) that people wrapped up in as needed

We just drove to a local place for brunch. However, there were less than 10 of us for our minimony.