Once a Drop Pod lands and the ramps open that's it...they stay open, from that point on the DP is treated as cover to anything hiding behind it. As the DP is a model in it's own right and not a piece of scenery the 'Intervening Models' rule is in effect (Page 21 Shooting Phase Rules)...so any model partially hidden from the firers view by other model/s receives a 4+ cover save.
, as a Dreadnought is a vehicle and not infantry at least 50% of it must be obscured by the DP from the majority of the firing troops for it to be able to claim the cover save.
Personally, I would say a Dreadnought behind a DP would be classed as 'Hull Down' to troops on the opposite side (if your opponents DP has all the ramps glued shut I would still apply this rule of thumb).
As with all things in this game, common sense is your best ally and if you really cannot decide between you roll a D6...1-3 obscured, 4-6 not obscured...simples!