You can, but it requires changing the server configuration.
Read the entries for AcceptEnv in sshd_config(5) and SendEnv in ssh_config(5).
update:
You can also pass them on the command line:
ssh foo@host "FOO=foo BAR=bar doz"
Regarding security, note than anybody with access to the remote machine will be able to see the environment variables passed to any running process.
If you want to keep that information secret it is better to pass it through stdin:
cat secret_info | ssh foo@host remote_program