Hello! thanks for playing!
The order the frogs appear in is entirely random, some frogs are rarer than others, though.

To be specific:
The way the game chooses which frog should appear is as follows:

The games chooses a random number between 1 and 4.
If the number is less than 4, a common frog is generated (common frogs include the default frog (1) leap frog (2) and slow frog (3)), 
however, if the number does lands on 4 then the game generates another random number between 1 and 10 to determine how to generate a rare frog.
if the number is less than 9 a common frog is generated
however, if it lands on 9 and if you've also lost a life the game will generate a heart frog, else if you have all 3 lives then you get a default frog.
if the number lands on 10 a golden frog is generated.

Does that answer your question?