During a cool rain on a hot summer day to enjoy the cooling sensation,

A. During a cool rain on a hot summer day to enjoy the cooling sensation, nature enthusiasts have observed that the frogs jump in the puddles.
Nature enthusiasts did not observe to deliberately enjoy cooling sensation that frogs generally (beware of the present tense!) jump into puddles. Also "have observed" may suggest that they are still observing, though one can also argue that present perfect is used to emphasize that the effect of their observation is still going on

B. To enjoy the cooling sensation during a cool rain on a hot summer day, nature enthusiasts observed that the frogs jump in the puddles.
Nature enthusiasts did not observe to deliberately enjoy cooling sensation that frogs generally (beware of the present tense!) jump into puddles.

C. To enjoy the cooling sensation during a cool rain on a hot summer day, the frogs jump in the puddles that nature enthusiasts observed.
puddles that nature enthusiast observed is a little bit shaky, using such a restrictive modifier kinda suggest that frogs jump in the specific puddles that nature enthusiasts observed

D. During a cool rain on a hot summer day, nature enthusiasts observed the frogs jumping in the puddles to enjoy the cooling sensation.
Modifier seems a little bit better here because nature enthusiasts may very well observed the frogs' jumping on a rainy summer day. However, second part suggest that nature enthusiasts observed XXX to enjoy the cooling sensation

E. Nature enthusiasts have observed that to enjoy the cooling sensation during a cool rain on a hot summer day, the frogs jump in the puddles.
Correct