An extremal horizon can be always embedded into spacetime as a Killing horizon but usually not uniquely. For example, extremal Reissner-Nordstrom and Majumdar-Papapetrou black holes are two different asymptotically flat spacetimes with the same geometry induced on their horizons. We consider an infinitesimal version of this problem—classification of connections admissible on the horizon in Einstein-Maxwell theory. We can interpret them as specific zero modes in the corresponding Near Horizon spacetime. Surprisingly enough, for spherically symmetric backgrounds those connections are basically unique unless we fine-tune the charge and cosmological constant. We also discuss how this uniqueness extends into the whole spacetime under an assumption of analyticity.