I love Skyrim. I especially love the horses. And I want Shadowmere to be my horse. I was just wondering if it is possible to have Shadowmere, and spare Cicero, while also destroying the 'Dark Brotherhood'.
There is no way to both destroy the Dark Brotherhood and obtain Shadowmere. If you choose to destroy the brotherhood (by killing Astrid in the shack) you won't be able to meet Cicero, and the quest progresses in such a way that you find the sanctuary and kill every single assassin present.
If you do choose to join the Brotherhood (by doing what Astrid asks of you in the shack), eventually Shadowmere will be given to you regardless of whether or not Cicero lives (if you spare him, you end up lying to Astrid). Every event from that point on will still happen (The Sanctuary gets destroyed), but the questline doens't end until you re-establish the Brotherhood in another location.
Cicero will never be introduced to you if you kill the dark brotherhood nor the horse will. So just do the Dark Brotherhood quest line and spare him. You should have access to Shadowmere either outside the Dawnstar hideout or by the one by Falkreath.