  This paper investigates the existence and uniqueness of solutions, as well as
the ergodicity and exponential mixing to invariant measures, and limit theorems
for a class of McKean-Vlasov SPDEs characterized by H\"lder continuity. We
rigorously establish the existence and uniqueness of strong solutions for a
specific class of finite-dimensional systems with H\"older continuous
coefficients. Extending these results to the infinite-dimensional counterparts
using the Galerkin projection technique. Additionally, we explore the
properties of the solutions, including time homogeneity, the Markov and the
Feller property. Building upon these properties, we examine the exponential
ergodicity and mixing of invariant measures under Lyapunov conditions. Finally,
within the framework of coefficients meeting the criteria of H\"lder continuity
and Lyapunov conditions, alongside the uniform mixing property of invariant
measures, we establish the strong law of large numbers and the central limit
theorem for the solution and obtain estimates of corresponding convergence
rates.
