Climate in Budapest is similar to that of other cities with continental weather at similar latitude (e.g. Paris, Vienna, Munich). It can be quite windy near the river Danube (next to the campus).
Note that in Europe, temperature is measured in Centigrade. Zero Centigrade is 32 Fahrenheit and every 10 Centrigrades difference makes another 18 Fahrenheit (i.e. 50 Fahrenheit is 10 Centigrade, 68 F is 20 C, etc).