Can the asset's hour meter automatically show up on a work order any time that asset is assigned to a work order

You can add it as a custom field.

Go to settings next to your name. Open features. Now click the link on Work Orders that says set preferences. Scroll down to customize work order forms and click custom fields. Here you can name your field and pick how you want it in your work orders. 

I put screenshots to show what you should see. Hope this helps.

​@James Beers that wouldn’t link the field to the asset meter though, would it?

​@Jesse Murphy This would be kind of tedious but you could try setting up work order templates for each asset that have the meter pre-attached.  You would then have to remember to use the template instead of the blank work order.  Another option would be to set procedure (and maybe asset) as a mandatory field on all work orders.  That would at least serve as a reminder whenever anybody creates one.

I believe that if the meter is linked to MaintainX, it will show the number under the hour meter reading box.