Hi Rob,
Snowy Mtns is my old stamping ground, moved to Port Macquarie for better weather last November. Learned to fly at Polo Flat with Mike Apps and then spent the next 5 years punching holes through the sky over the Snowies. So, I have some familiarity with most strips in the area.
The strip at Adaminaby (126.7), known as Kennedy Airfield, is privately owned by the local aeroclub group Snowy River Aviators. Your best contact their is Adrian Menhennitt who can give you a heads up on the latest conditions and preferred ops over the field. If you would like his email and/or mobile drop me a message. The strip is a lazy 20 min walk to the township of Adaminaby, or if you're lucky someone might be there to give you a lift. Options for accommodation and meals are lean pickings but you should be able to sort something through the net or with Adrian's help. The strip is grass and runs 09/27 which is good at this time of year when the winds are predominantly westerly, but if you park overnight chances are you'll have to clean off frost and ice before getting away in the morning. On my last flight into YADY in did note that the strip was becoming fairly rough from tufty grass, not a worry if you have strong gear and good sized wheels.
Polo Flat (118.1) at Cooma is a fairly good strip with a short sealed runway 18/36 and so close to town with plenty of accommodation and food choices that it's reasonable to call a taxi, or again if lucky get a lift with someone. You should contact Mike Apps for permission before landing there and he may have undercover parking available for you.
Cooma-Snowy (118.1), the main airport, is 17km out of town. This is where I was based, and believe me it is a very quiet airport, or at least was when I was there. So unless things have changed transport into Cooma may be difficult apart from hitching. The 2120m strip is all sealed but runs 18/36 so can be a problem with westerly winds. There is a 14/32 dirt cross strip which more often than not is less than helpful for avoiding strong cross winds, esp SW and if it's been raining this is sometimes unserviceable. Again, parking is all outside and subject to winds, frost and ice. Even though hangared under shelter (three sided shed) I often had to scrape away ice before an early morning flight, brrrrr.
Jindabyne (126.7) has recently had a new road-base surface put on their 12/30 strip so has improved somewhat from the really rough surface that it was. The cross strip 09/27 is rough tufted grass. Be careful here, the field is surrounded by hills and if the westerly is blowing it will be pretty rough and sudden sink is not unusual. Of course, Jindy being a tourist town, accommodation and food is aplenty but about 3km from the field. At this time of year prices are high as this is the beginning of the ski season, also it would be wise to book ahead for a bed. Same story with parking outdoors.
Cabramurra (the highest strip in Oz) is for emergencies only. I've not landed their but have driven on it. Apart from a relatively short sealed (kind of) section it is covered in long grass and has a few hidden holes. At this time of year you can expect it to be snow covered.
Talbingo strip is located right next to the Talbingo township and next to Blowering Reservoir. I have no idea what is available for accommodation or food. As has been suggested before this strip is controlled by Snowy Hydro Limited so permission should be sought first on 0264532888.
Khancoban, as has already been said, is fundamentally a Snowy Hyrdo strip but from the air looks in pretty good shape and easy to negotiate.
Island Bend? Forget it. Too much wildlife, too much scrub, wombat and rabbit holes and at this time of year probable snow. Also, I reckon the NPWS would be a tad unhappy. From what I've assessed when flying over it looks like a preferred place to crash in an emergency over the alps, and that's about all.
Geehi, same as Island Bend, except for snow.
So, in summary. The June LWE is start of ski season. Accommodation costs will be high. Safest alternatives for landing are Cooma-Snowy, Polo Flat, Adaminaby, Jindabyne and further afield there is Tumut, Corryong and Bombala. There are of course a few private strips here and there but a friend not so long back wrote of his CT tangling with power lines across the end of one of these, so you would have to be pretty sure of what you're doing before accepting an invitation onto one of these.
Watch the weather, as with anywhere but more so over the alps, winds and clouds can catch you out without warning. Only venture over the Snowies in calm, clear skies and then be alert to changes. BTW, it is stunning on a nice day, well worth the effort.
Hope this helps. Please contact me if would like more info.
Paul