Refugees do not look like being a problem; Ukrainians seem relatively easy to integrate.
Fuel prices are already skyrocketing; yesterday I saw petrol at eur 2,14/litre (it would be almost usd 9 per gallon), and a rise in prices in food and energy is expected.
If Russia's gas exports are cut, Italy has reserves for a few weeks. After that, I would expect some cuts to energy consumption mandated by law, such as lower heating temperatures or shorter air conditioning hours. We already had such things in 1973, including a ban on cars on Sunday (but petrol prices would be enough to rein consumption). According to some simulations, controlled blackouts could be necessary. But that would be in next winter.
If WWIII begins you would be marginally safer in the US (better missile defences) but not really safe anywhere. A thing nobody considers is that there are many intermediate degrees between a distant war and Armageddon; while Armageddon is unlikey (well, we hope so), getting back home in an emergency, even an intermediate one, is often a nuisance.