I would like to hide the number spinner on paper-input 3.x in all browsers. I'm currently struggling to hide it on just Firefox.
The solution described at the top here works on Chrome, but -moz-appearance: textfield does not affect the inside <input> element. I just adds an outline to the <paper-input> element.
return html`
<style>
paper-input {
--paper-input-container-input-webkit-spinner: {
-webkit-appearance: none;
margin: 0;
}
-moz-appearance: textfield;
}
</style>
<paper-input type="number" value="123"></paper-input>
`;
Results in: 
I also tried placing the -moz-appearance inside a mixin:
return html`
<style>
paper-input {
--paper-input-container-input-webkit-spinner: {
-webkit-appearance: none;
margin: 0;
}
--paper-input-container-shared-input-style: {
-moz-appearance: textfield;
}
}
</style>
<paper-input type="number" value="123"></paper-input>
`;
Results in: 
I created a glitch page to demo it (JSBin/unpkg don't work for paper-input 3.0): https://glitch.com/edit/#!/freckle-lilac
I'm not sure if I'm using the incorrect mixin, or if there's a simpler vanilla CSS way to fix this. The type="number" input is necessary for mobile platforms, but the spinner is not desirable for my use case.
After a day of tinkering around, I was able to solve my own problem. It looks like
var(--paper-input-container-shared-input-style_-_-webkit-appearance)is automatically set as the value for the<input>'s-moz-appearanceon Firefox.I was able to do this to remove the spinner on Chrome and Firefox, as well as fix the width issue that came up, too:
Demo: https://glitch.com/edit/#!/zippy-crime