Today the parks and gardens can be protected either as cultural monument according the Law on protection of monuments and historic sites or as the important landscape feature according the Law on protection of nature and landscape.
Park (garden) is the object of interest of heritage protection - as a monument it provides an evidence of historic development of the society, its art and culture, technique, science and life or it represents the evidence for the relationship to important personality or historic even. Its protection is in the interest of society.
In Slovakia today there are about 400 historical parks and gardens which are listed on the General Inventory of Cultural Monuments whici is run by Monuments Board of Slovak Republic.
Even the protection of parks and gardens can be differential in both cases it should be an active protection because the park as the cultural and biological element in the absence of protection and maintenance is very quickly losing its cultural and natural values.
The most relevant international document in this field so called Florence charter (1981), which was adopted by international council for historical parks and gardens (ICOMOS/IFLA) defines historical garden this way:
“A historic garden is an architectural and horticultural composition of interest to the public from the historical or artistic point of view. As such, it is to be considered as a monument.
The historic garden is an architectural composition whose constituents are primarily vegetal and therefore living, which means that they are perishable and renewable. Thus its appearance reflects the perpetual balance between the cycle of the seasons, the growth and decay of nature and the desire of the artist and craftsman to keep it permanently unchanged.
As the expression of the direct affinity between civilisation and nature, and as a place of enjoyment suited to meditation or repose, the garden thus acquires the cosmic significance of an idealised image of the world, a "paradise" in the etymological sense of the term, and yet a testimony to a culture, a style, an age, and often to the originality of a creative artist“.
The whole document you can find here https://www.icomos.org/en/charters-and-texts