Is it possible to reach Inari from Ivalo with public transport?

As long as you stay within Finland and travel between inhabited areas, you will be able to travel by public transport, although services may run only once per (week)day in some cases and you may need to take quite circuitous routes (travelling via a central town rather than directly from village A to B). You need to plan carefully to avoid potentially multi-day waits.

If you want to cross the border to Norway, Sweden, or Russia you are even more limited. There are some seasonal buses into Norway and Russia. Out of season, you're out of luck and a border crossing would require a potentially very time-consuming hitch-hike or very expensive taxi if you'd want to get into Troms or Finnmark. There are no border-crossing buses to Sweden. There are towns or villages that straddle both sides of the border, such as in Tornio/Haparanda or Karesuando, where you can reach both sides of the border with national buses and only a short walk in-between (or in some cases the bus drives maybe 1 km into the other country), but timetables are not at all connected. I remember trying to get from northern Sweden to the Käsivarsi region of Finland and giving up after realising I'd have to wait 23 hours for my next bus after walking the 500 metre from Sweden into Finland, so I brought a bicycle on the bus and cycled the final 100 km instead. The timetables are simply not designed with international travellers in mind, which may be reasonable for international bus travellers are very rare out of season.