The steed stone seems to make any piece of armor I wear weight 0 (i.e. not added to my encumbrance value). Since sneaking is based on how heavy the armor I'm wearing is, will having the steed bonus make my armor no longer penalized for sneaking?
Yes, it does help. I have personal experience with it, but no links to 'official' words on it.
The basis is that I wear heavy armor and sneak only on occasion, and noticed once I switched to the Steed, I was able to keep the 'running sneak' active around enemies much longer. My sneak skill is low 20s, and had not increased before I noticed. I do not sneak much, so when I do on that character I really notice the difference (I was actually removing all armor to try and sneak on him before getting the Steed stone).
As a side note, remember that weight is not the only thing that relates to sneaking. I have no perks on this character before OR after steed to assist with sneaking. But there are several available, as well as spells/potions.
Yes, having the Steed bonus will reduce, but not eliminate, armor sneak penalties.
Detection Value is made up of:
Sound is the sum of Movement Noise + Weapon Noise
Here's the equation for movement noise:
Source: Bethsoft Creation Kit