Approved wheel sizes will either be on the door pillar sticker or in the manual. If a different version of the same car has 15s I’d expect they are.
Assuming the 15s are an approved fit (here also says they should be -http://www.wheelfitment.eu/car/Hyundai/i30%20(2012%20-%20).html ) then no problem. The dealer is incorrect. No impact on ESP, ABS, speedo readings as the diameters are almost identical, within 0.4%
Just watch out with the nuts, you might need different ones if moving from alloys to steels and back. Think about your TPMS. Do you have pressure sensors in the wheels and a pressure readout in the car? Or is it just a warning based on mismatched tyre rotation speeds when driving straight. The latter is no problem.
I’m using winter approved all season tyres all year now - Vredestein Quatrac on my Santa Fe. They are as good as almost every winter tyre in snow and ice (fully tested by me in the Alps) , better on mild winter days and at season changeover, and only a small compromise compared to summer tyres in summer. Google all season tyre test for more brands.