Although there should be no problem with switching webmail clients, it is highly recommended that you backup your addressbook.
The suggested, easiest and quickest way is to export your contacts from the Contacts app in the cloud.
click on the three-dot menu to the right of the addressbook you want to export and select Download.
You will be asked where to save the file in your computer. Now you have a backup of your contacts.
The process of exporting your contacts from SnappyMail is pretty simple.
Login to SnappyMail;
go to Contacts;
click the three bars button and select Export (csv) or Export (vcf, vCard).
Exporting your contacts will take a moment, depending on the size of your address book. When it is ready, you will be prompted to save the file (contacts.csv or .vcf) on your computer. Please, save it in a safe place that you can remember later.
To import the addressbook previously saved:
select the file from your machine, click Import and finally Close.
To learn more about Contacts in Roundcube, you can check this tutorial