Height of buildings has been regulated in some semi-rural areas for the purpose of halting the spread of urbanization (as Dale suggests). For a concrete example, Orange County adopted some such regs, which included height of buildings... in 1935. The height of buildings has been part of the 1926 Standard State Zone Enabling Act (SSZEA) which served as template for many other laws that authorize regs on the height of buildings.
"Arbitrary and capricious" (which you suggested in comments might be a challenge to these) is actually a fairly easy threshold/test to meet, despite what its name might suggest. "We adopted these regs to stop the spread of urbanization" would almost certainly pass that threshold. Comparing the height of buildings with that of trees is a non-sequitur with respect to "arbitrary and capricious"; even arguing that "we want our trees to look taller so we limit the height of buildings well below that of trees" is something that would almost certainly pass the "arbitrary and capricious" test.
You might have more luck with a substantive due process test, whether (1) law & regulation "advances a legitimate governmental interest" and (2) it is "reasonable means to achieve that goal". But...
Most of the lawsuits regarding building/zoning regs have attacked interpretations of vaguer wordings like "harmonious" (with nearby architecture) on grounds of vagueness, when generally applied by the regulating bodies as "I know it when I see it". I haven't seen mention or discussion of height regulations being successfully attacked in their basic function. However, there have been some lawsuits based on the granting of special exemptions from general height regs though.
There is a height-related case predating zoning regs as such, namely Williams v. Paker 188 US 491 (from 1903) in which post hoc limits on the height of buildings was essentially judged constitutional ("we are of opinion that the statute in question cannot be adjudged in conflict with the federal Constitution"), even if it meant partially demolishing a building, as long as compensation was provided... sometime thereafter.
I think this might vary by state (constitution), but in New Hampshire at least, rational basis review is generally used for zoning regulations.
In so holding, the [NH Supreme] Court overruled two earlier cases to the extent that they don’t comply with the newly enunciated rational basis test: Metzger v. Town of Brentwood, 117 N.H. 497 (1977), which held that requiring 200 feet of frontage was unconstitutional where 123 feet “provided ready access,” and Powers v. Town of Hampton, 125 N.H. 273 (1984), which held that requiring a 24-foot wide fire lane was unconstitutional where 15 feet was sufficient. These cases factored a least-restrictive-means analysis into the rational basis test, which the Court has now ruled inappropriate.
I don't know of a (more recent) federal case involving zoning regs and some physical measurements, but in (1974) Village of Belle Terre v. Boraas a similar standard was upheld (7-2) at least on restricting dwellings to “one family”:
An ordinance restricting land use to “one-family” dwellings did not involve a procedural disparity, did not deprive any group of a fundamental right, and is rationally related to a permissible government objective. Justice William O. Douglas delivered the opinion of the 7-2 majority. The [US Supreme] Court held that the Village of Belle Terre’s ordinance restricting land use to one-family dwellings did not violate the Equal Protection Clause of the Fourteenth Amendment because the ordinance was not arbitrary, did not unreasonably apply to some individuals and not others, and was reasonably related to a rational state objective. The Court also held that the ordinance did not violate the Due Process Clause because it did not deny anyone a fundamental right such as the rights to travel, association, and privacy.
The neighbor nuisance argument on height (that you've also mentioned) mostly applies in areas without explicit (height) regs, i.e. it has been sometimes used as an ad-hoc substitute for lack of explicit height regs.
In summary, I think it will be an uphill fight to show that (uniform) height restrictions are unconstitutional, even in a rural area.
