Weather derivative markets, particularly Chicago Mercantile Exchange (CME) Heating Degree Day (HDD) and Cooling Degree Day (CDD) futures, face challenges from complex temperature dynamics and spatially heterogeneous co-extremes that standard Gaussian models overlook. Using daily data from 13 major U.S. cities (2014–2024), we first construct a two-stage baseline model to extract standardized residuals isolating stochastic temperature deviations. We then estimate the Extreme Value Index (EVI) of HDD/CDD residuals, finding that the nonlinear degree-day transformation amplifies univariate tail risk, notably for warm-winter HDD events in northern cities. To assess multivariate extremes, we compute Tail Dependence Coefficient (TDC), revealing pronounced, geographically clustered tail dependence among HDD residuals and weaker dependence for CDD. Finally, we compare Gaussian, Student’s t, and Regular Vine Copula (R-Vine) copulas via joint VaR–ES backtesting. The R-Vine copula reproduces HDD portfolio tail risk, whereas elliptical copulas misestimate portfolio losses. These findings highlight the necessity of flexible dependence models, particularly R-Vine, to set margins, allocate capital, and hedge effectively in weather derivative markets.