What does 勉強にレジャーに忙しい毎日 mean?


I was doing some reading practice in a Japanese intro book of mine and I can't
translate the second part of this sentence-

二人は去年の九月に日本語文化を勉強しに来日しました。最初は日本語の勉強で大変でしたが、今は日本語もだんだんわかってきて、 **勉強にレジャーに忙しい毎日**
をおくっています。

I'm a bit confused b/c of a few reasons. I've never seen an adjective used
prenominally to describe frequency/time expressions like 毎日. I don't regard
them as normal nouns cuz they don't really require a following particle so I
thought they were more like adverbs really. What does 忙しい毎日 mean here?
Everyday, which is busy? Can you use adj. for other time words like 寒い明日? Does
that even make any sense?

Also I don't really get how the に particles in「勉強にレジャーに」are being used here.
Are they making the preceding nouns into adverbs, a reason for doing
something, etc.

EDIT: I added more of the passage to put the sentence in better context.




> 勉強にレジャーに忙しい毎日をおくっています。

could be rephrased to

> 勉強したり、レジャーで遊んだりして、毎日忙しいです。

My English is not very good but let me try.

> I'm living a busy life working and playing.

"playing" here may not be a right word. Anyway the speaker is saying s/he is
spending life full of activities.




〜に忙しい is a set phrase meaning "busy with X".

