Despite the best efforts of reality TV shows to make "going tiny" look easy, the challenge remains for living legally
Short answer: No.
Longer answer with reasoning and points of consideration follows.
Trailer parks are zoned for modular housing (MH), which are a form of industrialized building (IB). Both of these groups are managed by government oversight for manufacturing. Modular Homes are 400 sf and larger, which falls under the purview of Housing and Urban Development (HUD).
Many tiny houses are considered home-built recreational vehicles (RVs), which are built under a set of industry adopted guidelines that are largely self-governing by bodies like the Recreational Vehicle Industry Association (RVIA). The two key documents that drive RV design are the NFPA 1192 (for standard travel trailers, 8'-6" or less) and ANSI 119.5, which is for park model recreational vehicles that are larger than 8'-6" in travel mode, and less than 400 sf (otherwise HUD get involved).
The "sticky wicket" for tiny houses is that... well... they're really none of the above. As a home-built RV, it wasn't produced in a certified manufacturing facility, nor was it under the preview of local building inspectors as its on wheels. Many tiny houses are built as well as conventional homes, which far exceed the standards for recreational vehicles (first word says it all, "Recreation" -- not a domicile).
Since modular homes are built to specific minimum standards for size and safety, there are areas set aside for their use as a residence (e.g. mobile home community or trailer park). Similarly, RVs are zoned for recreational use in campgrounds and RV parks. So, some RV parks will allow a tiny house to park there, but many areas around Richmond eschew the use of RVs as domiciles (folks called full-timers), and the codes are written to force folks to keep on rollin' down the road.
While the prospect of mobility is strong for many tiny house folks; many say its the uncertainty of long-term employment. Though many tiny house folks want a home and sense of place that's more than an RV park that's designed to pack 'em in side-by-side for the races. They want a real community and don't mind sharing less often used resources (like washers and dryers), though want a bit more privacy. And, in many cases, want something that's made to last, requires fewer resources to heat and cool, and is less taxing on natural resources like water (and waste treatment).
The "tiny life" isn't for everyone, but for many it's a reasonable solution to consuming debt and uncertainty that surround our lives. If you can give up the space, let go of the stuff, and live with people, places, and things that really matter, it might be time to consider if you too should take the tiny house plunge.
In any case respect for all in your lives.
Live Large -- Go Tiny! - Thom