Given a pencil of plane conics, one can ask how many conics in the pencil are nodal. The answer is three as long as the defining conics are in general position, which is a very special case of G\"{o}ttsche's conjecture. This work gives an equivariant enrichment in the Burnside ring of the classical count of nodal conics in a general pencil. Given a pencil of conics in $\mathbb{P}^2_{\mathbb{C}}$ which is invariant under a linear action of a finite group not equal to $\mathbb{Z}/2\times\mathbb{Z}/2$ or $D_8$, the weighted sum of nodal orbits in the pencil is a formula in terms of the base locus, which can be proved directly. Counterexamples for the two exceptional groups are also constructed.