have a great time是doing sth还是to do sth

have a great time后接doing sth.
have a great time doing sth. 做某事很开心/愉快例如
We have a great time preparing our own dinner.
“have a good time ”“have a difficult time”“have a hard time”等形式的词组后都跟doing sth.例如

I have a difficult time mixing work and pleasure.我很难同时兼顾工作和娱乐。
As usual, the police will have a difficult time.警察的日子照例不会好过的。
I had a difficult time trying a feather.我很费劲地摇了一下桨。

have a great time后跟doing sth.

have a great time doing sth. 做某事很开心/愉快

I had a good time visiting the zoo last Sunday .
上周日我参观动物园时玩得很愉快.

这个不一定的，如果事情还没有发生，就用to do
如果正在发生着，就是doing

have a great time是doing sth
如
They have a great time playing basketball every day .

是跟Doing something. Something=sth