IAH International Arrivals Question

I'm due to fly into IAH in a couple of weeks from Auckland, New Zealand, and have an overnight layover before coming back to IAH the next day to fly to London.

I've flew through IAH a couple of times (US Domestic onto New Zealand) so have never left the terminal. I know we will arrive into Terminal D or E, but I see that Terminal E is not allowing hotel shuttles to pickup because of construction.

So my question is, how easy is it to get to Terminal D or C from Terminal E arrivals to get to the hotel shuttles? Is it walkable with luggage or do we need to go down and get the subway?

Thx!