Seeing this post, I expected some of the Slovenian SP-members to answer, but since they haven't (not yet, anyway), I'll add my two cents.
I've only been to Slovenia once, and that was in August, but I've been all over the Alps, including some winter trips. High up in the mountains, in April everything is still very much in winter conditions. The temperature may well be above freezing, which means soft snow, but just as easily everything can be frozen solid. You'll definitely want to bring crampons. I would bring my ice axe too. And depending on the actual conditions I would also pack snow shoes (skis may be better, but outside the manicured slopes my skiing skills are not good enough). You'll have to find out what you need shortly before heading out. If you're going with a guide, he will know.
When I was on Triglav, there was no snow anymore. I found the ascent (
normal route from the Vrata Valley, via Kredarica and Planika) easy for a climber, hard for a hiker. There was a cable, and you can use it (I don't remember, but since it was there, I probably did). However, I would hardly call it a proper via ferrata; more like an easy scrambling route with a steel cable for comfort, and for security for the inexperienced and those that don't like exposure. Being comfortable with easy scrambling, you should find yourself well capable to ascend Triglav without cable. Based on all that, I don't expect real difficulties with snow and ice either. Depending on how much snow there still is in April, the cable can easily be buried. With a guide, he'll have you roped up then, at least on the final part of the ascent.
For my descent, I chose the
Bambergova route to Luknja and the Zadnjica valley. It was a fine route, but I'm not sure if that would be a good idea in winter: it's decidedly harder, in particular above Luknja. On some of the very steep secured sections I was glad I could use my via ferrata gear.
Finally, there is the route via Koca na Dolica, which is comparable to or slightly easier than the normal route from Vrata.
The nearest airport is Lubljana. Klagenfurt (Austria), is also conveniently close, but currently there are no direct flights to and from the UK. A little further away but with excellent train connections are Salzburg (Austria) and Venice (Italy).