Once a spigot starts freezing, better to force it open slightly or keep it closed?

Absolutely OPEN the faucet if there is still a drip! Use a tarp to divert water. I don't know your set up, but there are some universal homeowner truths here:

First, running water in pipes almost never freezes. Stoping the flow will make the freezing faster.

Next, and very important, is that once a spigot is frozen, the water leading to it will freeze, causing broken pipes.

Most importantly, stop thinking that the pipes inside your house are all you really have to worry about! When your spigot freezes and then the pipes under your yard freeze, they are almost guaranteed to burst. It is very expensive to have a backhoe come and dig up your underground pipes, possibly all the way into the street (where your pipes connect to the main).

It sounds like you are in for more below-freezing weather. Be pro-active and let both hot and cold water pipes drip a steady stream. The water may seem wasted, but it is nothing compared to the geyser you will have if a pipe breaks!

Open it and let it drip. You can buy a foam insulating cover for an outside faucet. When the weather gets nice and you have the means, I would replace it with a frost free faucet.

If you can open it a bit but it's frozen, thaw it ott with a hair dryer.