How to cherry-pick from a remote branch?

Question

Since "zebra" is a remote branch, I was thinking I don't have its data locally.

You are correct that you don't have the right data, but tried to resolve it in the wrong way. To collect data locally from a remote source, you need to use git fetch. When you did git checkout zebra you switched to whatever the state of that branch was the last time you fetched. So fetch from the remote first:

# fetch just the one remote
git fetch <remote>
# or fetch from all remotes
git fetch --all
# make sure you're back on the branch you want to cherry-pick to
git cherry-pick xyz

Just as an addendum to OP accepted answer:

If you having issues with

fatal: bad object xxxxx

that's because you don't have access to that commit. Which means you don't have that repo stored locally. Then:

git remote add LABEL_FOR_THE_REPO REPO_YOU_WANT_THE_COMMIT_FROM
git fetch LABEL_FOR_THE_REPO
git cherry-pick xxxxxxx

Where xxxxxxx is the commit hash you want.

Adding remote repo (as "foo") from which we want to cherry-pick

$ git remote add foo git://github.com/foo/bar.git

Fetch their branches

$ git fetch foo

List their commits (this should list all commits in the fetched foo)

$ git log foo/master

Cherry-pick the commit you need

$ git cherry-pick 97fedac

After merging a development branch to master, I usually delete the development branch. However, if I want to cherry pick the commits in the development branch, I have to use the merge commit hash to avoid "bad object" error.