Possibly. You introduce the potential of some condensation if you attempt to insulate the interior. You'd be better served to insulate the exterior.

Agree with WOW that you are better off insulating outside versus inside, but consider a lot thicker foam than 1".

From reading your question are you only looking at covering the glass panel or the whole door?

Simple fix, put up some vertical cellular/honeycomb shades. Now here's the reason: it traps the ambient air in between the shades which provides natural insulation. Plus, as an added benefit; it looks way better than having to put up some type of foam board.

Except that blinds are not airtight. And in doing such, do not allow for air/energy to warm the interior surface and allow the surface temperature to get to dew point. Dew Point = condensation.

Years ago we had a thermal roll up shade on door. and i put a sliding storm door on too. we let dog out that door so it was used a lot. i replaced slider with a french door and got rid of roll up and storm door. we havent used room in 10 yrs.