Do I have to roll damage for each of them seperately? 

If I tag a Horde using a Heavy Flamer with C&P as a Devastator, do I need to roll damage 20 times? That seems excessive to me, I dunno if I want to roll that many dice at once. 

How my group does it is note the minimum damage and penetration from a given weapon. Say a boltgun at D10+9, pen 4, has a minimum damage of 10. If those figures automatically beat the given horde's toughness and armour, then we don't bother rolling. That hit is going through whether it's one wound or ten.

Technically, yes, you do need to ensure that the hits deal damage. Generally, we're luck enough that most hordes will always take one point of damage vs. even the most basic of marine weapons.

If you're unlucky enough  that it does not, I would then determine the minimum die value it takes to deal a point of damage, and use probabilities to get a rough number of how many hits it would take.

Example: If firing a 1d10+5 damage weapon, and I need 7 damage total to hurt the horde (3 or higher on the damage dice), I would assume that 70 percent of my hits damaged the target. If I got three hits, I would multiple 3 by .70 and round fractions to the nearest whole number. In this case 2.

A bit messy, but can avoid rolling all that damage. Also, if you are rolling it, ignore righteous fury.

It's another reason I find the errata makes the game more fun: the minimum damage on many weapons such as the bolters was raised. So most hordes will be automatically injured even with weaker shots from them.

Decessor said:

That is pretty much what we do.  The first time I ran a game, I missread it, and thought that you had to cause a minimum of 15 damage, but instead they were just using 15 as an example.

As a GM, part of my prep is figuring out the minimum roll possible to damage each of my hordes, then figure out which weapons will make that automatically.  A little bit of prep time before the game saves a LOT of dice rolling during the game.