As it turns out, vue-color does not support server-side rendering, which is where nuxt.js is running into problems with this component. You'll need to render the component only on the client-side, which is slightly more involved than importing directly to the file.
First, you'll want to create a new file in your plugins directory called "MyPlugin.client.js". By adding that client.js part, we are telling nuxt.js that this plugin is only to be rendered on the client. (Note: There is also a .server.js extension for server-only rendering).
In this file, we'll need to add our picker of choice to our project with the following
import Vue from 'vue'
import { Chrome } from 'vue-color'
Vue.component('chrome-picker', Chrome)
Save this file, then we're going to need to import that in our nuxt.config.js. In that file, find your "plugins" and add the file. Your plugins property should like something like this
plugins: [
{ src: '~/plugins/ColorPicker.client.js', mode: 'client'},
],
In this case, "mode: 'client'" is slightly redundant, as we've already specified to nuxt that our plugin is client only with the .client.js extension - I just add it in for good measure.
Now, to reference our new component, we'll add the following code inside our html
<client-only>
<chrome-picker :value="primaryColor" @input="updateColor" class="colorPicker"/>
</client-only>
Your vue-color component should now be rendering as planned. I hope this helps some people struggling with this, as I was very confused myself.