You can descend to any height for the purpose of a landing, on an unpublished instrument approach.
It would be correct to say that you can descend to the appropriate minima on an unpublished instrument approach.
There is no requirement for private instrument approaches to be published.
However, to be classed as an instrument approach, it would have to conform with the requirements of ICAO DOC 8168 which deals with the design of such procedures.
Dreaming up a convenient track from a local VOR towards your runway / strip is not an instrument approach procedure.
If you want to have an approach procedure at your strip you need to;
1. Have a full obstacle survey - Expensive.
2. Have the procedure designed by a qualified procedure designer - More Expensive
3. Have the procedure crosschecked - just as expensive as in 2.
4. Have the procedure flight checked by an approved organisation
and a few other admin bits gets you a private instrument approach procedure.
Having done so you can not complete the procedure unless you know the weather it at or above the applicable minima........therefore you need weather reporting (the US ASOS or AWOS expensive type of equipment could do)
So the question is.........do you spend enough for year round parking / landings and chaufered limo from your nearest regional airport to justify spending more on a private instrument procedure.........that you will use 10 or 12 times per year?
To sum up -
A instrument approach meets the requirements of ICAO DOC 8168 including survey etc. If you do not have evidence of that then you do not have an instrument approach procedure.
Regards,
DFC