I've been there at Christmas,some years ago...and there was plenty of snow.
I travelled by public transport,train and bus..and as I remember everything was working fine,no problems.

Thanks a lot for your answer!
Yes, we already figured out that a car is not necessary when traveling on the carribean side. Also I informed myself already that Tortuguero and Corcovado are not accessible by car.
Our itinerary Looks like this now:
Flight to San José
San José - Tortuguero
Tortuguero
Tortuguero - La Fortuna
La Fortuna
La Fortuna
La Fortuna - Sámara
Sámara
Sámara
Sámara - Santa Elena
Santa Elena
Santa Elena
Santa Elena - Manuel Antonio
Manuel Antonio
Manuel Antonio - Uvita
Uvita
Uvita
Uvita - Corcovado
Corcovado
Corcovado
Corcovado - Cahuita
Cahuita
Cahuita
Cahuita
Cahuita - Puerto Viejo
Puerto Viejo
Puerto Viejo
Puerto Viejo
Puerto Viejo - San José
Flight back home from San José
I thought about renting a car from La Fortuna until Uvita or Drake Bay.
From San José to Tortuguero and from Tortuguero to La Fortuna I thought about either booking a privtae Transfer/shuttle or to have an organized package (for example a two nights stay with Transfers to and from Tortuguero plus a tour through the park) by one of the lodges there. If possible and not too costly we might even fly from Tortuguero to La Fortuna.
In La Fortuna we would then take our rental car until we leave it in Uvita or Drake Bay (depending if we decide to stay in a hotel in Drake bay or in a lodge inside Corcovado). If we decide for an organized package from one of the lodges inside Corcovado we'll probably drop the car in Uvita and have them organize the Transfer to their lodge for us.
From Corcovado to Cahuita we would prefer to fly (I know that there are no flights from Corcovado, but there should be some from Puerto Jimenez or Drake Bay). If that is not possible we'll have a shuttle or private transfer arranged.
I figured that from Cahuita onwards we could move either by bicycles or public transportation.
Does this make sense or did something important slip my mind?
I hope to visit Biosphere Reserve Askania-Nova next April. Is the tour out on the steppe where the zebras and other animals run free (not in zoo) easy to arrange if I just show up in the town of Askania-Nova? And what is the best way to get there by public transport from Odesa....or should I seek bet transport to there from Kherson. Thank you very much.