Narita airport to Hakone by rental car

We are a family of six with my aged mother. 1st time to Japan. Renting a car with GPS. Is it easy to drive from Narita airport to Gora, Hakone? How much is the toll charges? In mid January, would the road be icy and any precaution required?
My wife is discouraging me to drive however, felt that train transfers to Hakone may be challenging. Appreciate advice.

Is Hakone (Gora) is the first destination after you arrive in Japan, no stopover in Tokyo itself? To go from Narita to Hakone, you'd need to drive "through" Tokyo from east to west... and mid January there may be some icy roads around Hakone. Roads in Hakone can be quite crowded on the weekends (though I don't know exactly when you are coming).

I would also recommend public transportation. You could go Narita Airport via JR Narita Express to Tokyo or Shinagawa, then taking JR Tokaido Shinkansen to Odawara, then Hakone railway and other local transport to Gora. Or you could go Narita Airport to Shinjuku (alsovia JR Narita Express), then Odakyu Railway (get reserved tickets) Romance Car to Odawara/Hakone-yumoto, then local transport to Gora.

Public transportation is easy to deal with in Japan, you just need to read up on things a bit. So unless your mother has trouble walking or standing (on train platforms, waiting for trains, or walking up a bit of slope when you change between local transport modes in Hakone), trains are the way to go.

If you have to ask. Then don't do it.

Thank you for the response.
With a car, movement is much easier as we spend 3 days 2 nights at Hakone. Staying at Gora will mean a lot of travelling time. Also in winter season, afraid the waiting time for bus/train may be long and cold.

Whom says movement around Hakone will be easier by car?

Getting around Hakone by car is very convenient outside of weekends and holiday periods. But it is not pleasant during the high seasons. Then again, other means of transportation aren't very pleaseant during the high seasons, either, especially buses.

Mid January will not be crowded, especially on regular weekdays. There is a small chance of snow and ice on the road, though.

Thank you, Uji. Very re-assuring.
Arrival to Narita is on Tuesday morning then proceed directly to Hakone.
My major concern is driving on icy road. No experience at all. Renting a mini-van.

While driving in Hakone is convenient, driving through Tokyo can be very stressful. I personally would rather take the train to Odawara and rent a car from there.

My major concern is driving on icy road. No experience at all.

Then, I recommend to cancel your rental car reservations in case weather conditions are very wintery during your stay.

Also note that public transportation around Hakone is very convenient, especially on regular weekends when often it is not very crowded.

I don't think so.
But depends on date,flight arr time and weather condition.

No need thru mid Tokyo as fastest route.
Via "Wangan line(bayshore route)" is not so hard if 1st timer as escape mid area.
https://goo.gl/maps/YpubTNDzmh22
https://youtu.be/t32u8UWJGlM
(10:30 - 28:00 : half of Wangan line https://goo.gl/maps/AdA1R3bp1hz )
Also easier via "Aqua line" route with short break at "Umi-hotaru"
if super fine weather and no strong wind.
(strong winds make bridge section close long time)
https://goo.gl/maps/s3iSajfRCt52
https://youtu.be/Y5-wQ12jcdg (opposite way W to E)
https://www.umihotaru.com/en/

ExpWay toll fee : about 4500Y(via Wangan line)
Gas/fuel : around 15L (around 115Y/L today)
And if rent a car return spot won't be same need "one-way" option fee plus.
(Read rent a car web)

Hakone is higher ground/colder than lower ground/warmer mid Tokyo.
But about snow fall or not depends on weather.
Not everyday dangerous but just not everyday safe.
Watch one-week forecast and Raod live cam.
http://weather.yahoo.co.jp/weather/jp/14/4620/14382.html
http://www.hakone.or.jp/web-camera/ (click pics)
Order Studless(winter) tire recommend.

And you have to study all(after P19) if really thinking drive Japan.
http://www.hkd.mlit.go.jp/topics/toukei/chousa/h20keikaku/e/e_all.pdf

Awesome Adnwg. Very informative and very thankful to have your inputs.
Uji - will take your advice on rental car cancellation closer to the date of travel.