Being a former park owner I can tell you that you should look at the park rules or sometimes the lease. If the park looks very neat and organized it probably has a complete list of rules that are enforced. If the park looks kind of dumpy then it may have few rules or the rules aren't enforced.
I've never seen a park that didn't allow washers inside. Often each home is metered for water so the amount of water used is not an issue for the park owner. It is still possible that they have the rule so you have to check.
As far as a hot tub, the same things goes..check the rules. I don't think I would start bending the rules. If you have a stict park you might find yourself facing an eviction. Then you have to figure how are we going to pay for a lawyer, pay to move the home out and where are we going to move it to? Normally a park owner evicts the tenant, but also the home has to be moved off the premises.

First, I guess it would depend on which state/county/city. Then you have the "park rules". Check the CCR's

Is this a new park, or an established park?
If established, does anyone else have hot tub spa? And even if so, doesn't mean YOU can. As parks rules change - sometimes if something has been the preceeding the rule change, it may be able to stay. Would not apply to new owners.
I'm thinking, if no-one else has one, they probably aren't allowed. Liability/Insurance would be a big factor here.

Realistically - what you can and cannot get away with: (Like I said, maybe it depends on where), but to be blunt, in SoCal...NOTHING! It's either the Management or, most likely the "NEIGHBORS" who complain to the Managemet about what everyone else is doing!

My sister's MIL was a mobile home owner, then Manager in a mobile home park. (I knew her well, as I lived with her for several months prior) OH MY GOODNESS - the stories she had to tell! "Best Friend Neighbors" secretely complaining on each other.lol).

My MIL lived in one, my SIL lived in one. My Step-Daughter lived in one. Believe me, we've heard enough stories!

Even I myself, was so fed up with renting, I had considered a mobile home. Went to look at a few. I remember while going thru one, I glanced out the window and there was this HUGE FACE staring at me! (It was the man next door staring to see what's going on - from inside his own!) That did it for me! NO WAY could I every buy this and feel comfy, and have PRIVACY!

I also found that all utilities are paid to the park. (As SIL had to do - contact the Dept of Weights & Measures to have her gas & electric meters calibrated. apparently many in the park were not properly calibrated - causing higher energy charges)

Don't "assume" you can get away with anything. The "neighbors" will tell on you!
The best thing is to get the park rules, and expect to live by them, or not live there at all. It doesn't take long to be ratted out.

Well, at least that's sorta how it is in Southern California!

Oops! Forgot. Here in SoCal, most mobiles come with washer/dryers.

Only bad thing here...all the "single-wides" have been becoming extinct. For some reason, SoCal decided to do away with single-wides. I see them all the time advertised "for sale", but "must be moved". (And most city ordinances will not allow them to be moved on your personal property in Calif.)

In defense of park owners, many areas have oppressive mobile home and mobile home park ordinances which hold the park owner responsible for everything that is considered to be a violation of any provision of such ordinance, including certain actions of tenants. Some of the enforcement officers really stretch to make things tougher. So a lease provision requiring the tenant to comply with all local, State, and Federal laws may be necessary for some protection of the park owner. Many of these rules discriminate against the poor, but the so-called champions of the poor do not get involved. No money in it for them.

I would not want to put a hot tub in your backyard, if you are moving into a park (or manufactured housing community as ours is called) there will no doubt be children. It is a major liability and your insurance co. will probably say no way to that (my insurance co. actually checked the depth of the kids wading pool) We have lived here for 5 years and if I had known some things before I moved...

Look around your park carefully. look for signs of things that would bother you before you move there. Check the neighbors property on either side of your lot, basically look for trash (roaches just love mobiles) and if it looks like they keep their lawn manicured or not. If you have children, look to see if it appears your neighbors have kids (good either way, if you don't want to live next to children it is a heads up)
If you are buying a new mobile it will come with a washer and dryer (well it should anyway) some even come with furniture (not the sturdiest stuff in the world, lasts about a year)
never heard of them not letting you have washers in your home.
If you are worried about privacy (because yes, every park has their peeper seems like) mini blinds work wonderful.
just read over the list of rules in your contract very carefully, and if they don't have a list of rules?? I would most definitly not move there.
oh and another thing, when they quote you the price for the lot rental, be sure to ask them when the next rent hike will take place and how much it will be (we never factored that in when we moved) ours goes up 10.00 every year.
Also we live out of city limits, so there isn't any 'city rules' that we have to follow, it is almost like living in the country (or a compound, however you wish to look at it:) rules are more relaxed here than at some of the ones we looked at in the city (one did not allow any window coverings of ANY kind, how are you suppose to get dressed and sleep and umm...... without the neighbors seeing you??)
that one was a joke, the rules was in a 100 page manual.