Does Blender have a way to reduce texture size? I have several objects, each with 1024x1024 textures on them. I want to reduce that to just 64x64 per object, for performance reasons (I'm planning on having a lot of these objects).

I'm not worried about losing quality, since the textures are simple and I'm going for a low-poly, pixelated look.

Does Blender have a way to automatically reduce texture size, or do I need to edit the texture in GIMP, then reapply it to the object?
Create a separate project, import the textures into the VSE as an image sequence, lower the dimesion values to 64 px by 64 px, and render them all out as .pngs or your preferred image filetype.

Though as NoviceInDisguise, Timaroberts and Galih Bagaskara have already said, this is probably best handled by GIMP or some other dedicated graphic editor. Using the method I described, every texture will lose its individual name once rendered, which may or may not be important to you.