Talking about the weather is a must for the British so there’s no reason why you shouldn’t be able to do it in Greek. To start with here are various phrases you could use to ask about the weather (ο καιρός/Ο ΚΑΙΡΟΣ):
Τι καιρό κάνει;/ΤΙ ΚΑΙΡΟ ΚΑΝΕΙ;
or
Τι καιρό έχετε;/ΤΙ ΚΑΙΡΟ ΕΧΕΤΕ;

These literally mean, “what does the weather do?” and “what weather do you have” and are both ways of asking what the weather is like. If you want to ask about what the weather has been like switch the verbs to the past tense to get:
Τι καιρό έκανε;/ΤΙ ΚΑΙΡΟ ΕΚΑΝΕ;
or
Τι καιρό είχατε;/ΤΙ ΚΑΙΡΟ ΕΙΧΑΤΕ;

Another different way to ask about the weather might be, “How is/was the weather?”, which is:
Πος είναι ο καιρός;/ ΠΟΣ ΕΙΝΑΙ Ο ΚΑΙΡΟΣ; (present tense)
Πος ήτανε ο καιρός;/ΠΟΣ ΗΤΑΝΕ Ο ΚΑΙΡΟΣ; (past tense)

And then perhaps some answers would be:
 

English	Lower	Upper
It's cold (lit."it does cold[ly]")	κάνει κρυό	ΚΑΝΕΙ ΚΡΥΟ
it's hot	έχει ζέστη	ΕΧΕΙ ΖΕΣΤΗ
the weather is good	ο καιρος είναι καλος	Ο ΚΑΙΡΟΣ ΕΙΝΑΙ ΚΑΛΟΣ
it's raining	βρέχει	ΒΡΕΧΕΙ
it's snowing	χιονίζει	ΧΙΟΝΙΖΕΙ