You can say the sentence with or without "do," but it will mean something different.
How many rooms have conditioner?
is a simple question; you are asking which rooms do, and which rooms do not, have conditioner in them.
You would never ask:
How many rooms do have conditioner?
unless it had already been established, earlier in the conversation, that some rooms did not have conditioner, and you want to establish a definite distinction between the set that do and the set that do not. For example: you could say:
Joe, we have a problem--I just found out that housekeeping forgot to put conditioner in some of the rooms?
Really? That's terrible! Well, how many rooms do have conditioner?
But you would not use "do" in a conversation like this one:
Let's check the inventory of the rooms. They all have shampoo, and they all have conditioner.
Simply put, only use "do" in a construction like this if you're using it in opposition--express or implied--to "don't." A good rule of thumb is: if you couldn't use "do" on its own, don't use "do" with a noun. So you might say:
This room doesn't have a television. How many rooms do?
or:
This room doesn't have a television. How many rooms do have TV?
but you wouldn't walk into the room and ask:
How many rooms do?
without the first part of the sentence--it wouldn't make sense. So you can't use "do have TV" on its own, either.
Also: I suspect you're also using "conditioner" wrong. "Conditioner" on its own is an uncountable noun, referring to a hair product that you use after shampooing.
First I used the shampoo, which smelled fine. Then I used the conditioner, which made my hair smell like eels!
I suspect you meant to say "air conditioner," a machine used for cooling air inside a building. In English, "air conditioner" can be shortened to "A/C" or in some cases "air," but never to "conditioner."
"Air conditioner" is a countable noun, so in your sentence you would have to say:
How many rooms have an air conditioner?
or, more idiomatically, you could use the uncountable version: "air conditioning":
How many rooms have air conditioning?