Yes it is possible to build a structure similar to what you describe, and this is exactly what some researchers use to study cloud formation and the processes that operate within them. The other answers and comments have established that re-creating full-scale weather systems is probably out of the question, but meteorological cloud chambers exist for recreating certain weather phenomena. You ask about "preferably consumer grade" examples, but since all of these types of apparatus are effectively custom built to an extent, you could potentially create a "consumer-grade" version (just don't necessarily expect research grade data from your efforts!).
From a research point of view, they are used mainly for studying microphysical processes within clouds: condensation of ice nuclei, chemical interactions between molecules in clouds, snow formation, ice-crystal riming, thunderstorm electrification, and so on. As you point out in the question, the down-scaling issue means they aren't suited to reproducing large-scale weather features, although the limit is as big as you care to build it I suppose...
Here's a link to a research grade ice cloud chamber, used at the University of Manchester, UK. There are some excellent photos of how it is put together (unfortunately I don't have permission to put them here). Essentially it is a 10m tall steel chamber, which can be cooled down to about -55 centigrade. The pressure can be lowered to simulate conditions in the upper troposphere (about 50hPa). It has been used on occasion to reproduce the conditions in thunderstorm electrification.
Here's a video of a home-made cloud chamber in action (again, it is imitating small scale features and processes in clouds, not weather systems per se.), and a simple diagram of how it is set up:
Alcohol is used here, since it evaporates and condenses much more readily than water. The dry ice at the base cools the lower section of the chamber, creating a temperature gradient within the chamber. The alcohol droplets will evaporate from the strips forming a fog (cloud) at the top, then condense as they hit the cool air, forming gentle rain droplets nearer the base. Here's a link to more detailed instructions.
Something in between these kind of set-ups is the closest you will come to re-creating 'real' clouds at home. They won't have the beauty of a towering cumulus over a mountain range (although some say there is beauty in cloud microphysical processes.)
Annecdote 1: At the EGU 2014 Annual Conference in Vienna, the organisers created a series of rooms that you could walk through and experience being inside a cloud.
Annecdote 2: Incidentally the first person to create a 'weather chamber' was CTR Wilson, trying to reproduce the cloud formations he had seen on Ben Nevis in the Scottish Highlands. His invention actually led to the discovery of ionizing radiation.