This is "opinion only" - I cannot speak with authority on specifics but, I have visited Singapore a number of times (4 or 5?)and the following would be what I would expect based on what I have seen there and elsewhere in Asia:.
While I have seen the downturn in Asian public activity immediately after Chinese New Year (even Hong Kong gets very quiet) I'd expect this to be more related to the number of people seen in public than in major attractions open.
You can almost certainly check on a website by website basis but in Singapore I'd expect you could see "Chinese Garden" (very good gardens)(get off train at 'Chinese Garden' :-) - walk directly into gardens ),
the impressive new high tech gardens in town (I've not seen them yet),
Bird Park. ... similar.
Sentosa Island is ALWAYS willing to take your $ (horrible place :-) ).
I'd expect areas like Little India, Arab Street,...to be lower populated but odds are that shops would be open and selling food.
Some temples may be less populated but probably still able to be accessed as much or as little as ever.
Mosque in little India is the most 'tourist friendly' & "laid back" I've seen anywhere (I'm Christian but I (very politely) 'evicted' rowdy tourists from the Mosque on one occasion when the locals just ignored their rudeness).
Marina Bay will still probably take your $ so you can go up and see their infinity pool and view.
Overall I'd expect that the island would be "slow" but that there would still be lots to see and do if you are only there for a few days. –