On my Kindle, I incur a $4.95 charge per week for using it abroad, if I turn on the wireless function.So I make sure I download all the books I want before I leave. On a 3 month trip, I did pay the weekly fee so I could download the NY Times every day.
Sorry I don't know a specific Fire response.

The Fire operates on wifi signal, so where you have wifi you can connect.
Kindles that do not have wifi use the cellphone system for data transmission, so that's my guess as to why you'd have to pay for plain Kindle to receive overseas (Amazon eats the cost of data transmission in the US).

Technically, the Kindle Fire is capable of operating where there is WiFi access.

Operationally, there are more to it.
1. Power: you need a USB charger plus a plug adapter.
2. Know how to configure your WiFi. Unfortunately there are many ways WiFi is offered to you. Some simple as open WiFi and connect to the offered service. Some you get redirected to some legal pages and you have to agree to the terms with some kind of identity, your room number, etc, before they let you access sites other than hotel site. While some require you to fill out the WiFi configuration page and enter the key provided by the hotel, etc. in order to connect to the server. If you have done this in the US, it is not much different in Italy except if you get redirected, you might not be immediately given an English version.
3. Beware of look like WiFi network names. In a busy place, you are given many choices of network to use. Some are legitimately offered by the hotel, etc. while others might be trying to lure unsuspecting guests into connecting to password capturing server site. I always ask hotel exactly what is the name of the Wifi network offered by hotel.

Hi Maggiemay2012:

I used my Kindle Fire to check emails and browse the web several time this past May in the Tuscany region as well as in the Bolgheri area. Went to "settings", turned the wi-fi feature on, and it automatically found the hotel's wifi. Selected connect, entered the password, and all worked great.
Biggest problem for Kindle Fire is that it requires wifi. Previous Kibdle versions used Whispernet (cell), so you could download just about anywhere. All in all I had no problems with the Fire, as long as you have wifi.