Is it possible to summon zombies with lowered arms in Minecraft?

1.13+

I don't think it is possible to make zombies not raise their arms. I would suggest retexturing items that armor stands can hold/wear (boots, leggings, chestplate, helmet, sword, bow...) using CustomModelData to look like body parts/clothes and use this website to summon them with a particular orientation/pose. This of course requires a resourcepack and some commands, but it is probably the option that gives you the most flexibility.

1.8-1.13

The void of no knowledge. Someone please fill it.

1.8-

Once upon a time there was a hostile "human" mob which could be summoned up until 1.8, and looked like the player. Using mods or external tools it may be possible to retexture it to work in later versions, but I'm not sure how. Obviously in versions prior to 1.8 you can just use that. Anyone with information on that should edit it into this post.

In the custom npcs mod you could set the zombies job to "puppet" and manually lower their arms to whatever position you like. However it will stay in that position even if its attacking.