Learn Croatian: Ovo osvježavajuće piće je vrlo hladno.

It comes from the imperfective verb osvježavati (to refresh). First, you take the 3rd-person plural present tense, which is osvježavaju (they refresh). Then you add the suffix -ći to make the present active participle: osvježavajući. When used as an adjective, it declines to match the noun.

Why does osvježavajuće end in -e in this sentence instead of -ći?

Because it is modifying the neuter noun piće in the nominative case. The base participle form osvježavajući acts as the masculine adjective form. Because it ends in a soft consonant (ć), the neuter nominative ending is -e instead of -o, giving us osvježavajuće.

How would this participle change if the noun was feminine, like limunada (lemonade)?

Just like a standard adjective, it would take the feminine nominative ending -a. The phrase would be ova osvježavajuća limunada.

Could we build this adjective from the perfective verb osvježiti instead?

No. The present active participle can only be formed from imperfective verbs. Because an action must be ongoing to happen continuously in the present, perfective verbs like osvježiti cannot be used to make this form.