Q:

Make Hair Particles Glow or Emit Light

I know you can make objects glow or emit light with an Emission node, but can you do this with hair particles, too?

A:

Absolutely! Just make sure the material option in the particles tab is set to the material you want, whether that be an emission shader or a hair shader.
Keep in mind that the material setting is a selection based on your objects material slots. If you select one of them, it will use that material, even if no parts of your mesh are assigned to it.

A:

Idle Chit-chat
I can think of one simple, easy, two-part solution that produces something like the following result with no lighting except one point lamp at Emission: 100.

Solution
Part 1
Select the object that will emit the Hair Particles. Go to the Properties panel > Materials tab and add a new material. Name it "Mesh." This will be your mesh's material. Customize it as you will.
Add another material. Name it "Hair." This will be your hair's material. Set it to a Mix Shader with a Fac: value of 0.3 (you can adjust this to your liking), Hair BSDF in the top input, and Transparent BSDF in the bottom. Adjust the Hair BSDF's settings as you will, but make sure that the color is roughly similar to the Emission node's (brown and yellow, red and orange, yellow and white, et cetera). The Transparent BSDF should be pure white. Plug an Emission node into the Volume output. Set the Hex Color Value to F5FF4D. The Strength: can also be adjusted to your liking. After this, your material nodes might look something like the following.
Sample mesh material nodes (totally random; adjust to your material):

Sample hair material nodes (to my formula; adjust some things to your liking):

Part 2
Go to the Properties panel > Particle systems tab > Render dropdown. In the Material Selection slot, make sure Hair is selected. It should look something like the following.

If you so desire, you can examine the following .blend file, which includes the cube and hair from the top. You may have to resimulate the hair, though. Do this by keying Shift + LeftArrowKey to go to frame 1 and then keying Alt + A to cache. Let it cache until frame 31 (the frame I rendered).

