Mount Fuji view and trip

In feb 2017, me and my boyfriend visit Tokyo's surrounding area. And one of the destination that we are considering is Hakone (in order to see the Mount Fuji and hot spring). To get to Hakone-Yumoto, we will take the bullet train (SHINKANSEN KODAMA 681) for 35min.

I'm wondering if with the bullet train we are able to get a good view of Mount Fuji. And is it a good idea to go there during the month of feb and what guys would recommend as activities?

Thanks ahead.

1)
Only 3 points and not so long use google translate.
http://asuzuki.la.coocan.jp/yama/yama2/tokaidou2.htm
https://youtu.be/DNvBuM6bcVg

2)
Read Hakone Navi.
http://www.hakonenavi.jp/english/

Shinkansen will take you to Odawara station. From there you will need to take another train to Hakone Yumoto (a short ride). Odakyu Romance Car (not Shinkansen) can take you all the way to Hakone Yumoto.

To view Mt Fuji from Hakone, you will have to go high, near where Lake Ashi (Ashinoko) is. My favorite spot is from Narukawa Museum, on south shore of Lake Ashi.

If you want to view Mt Fuji from Shinkansen, you will have to travel further west.

This site has lots of good info: http://www.hakonenavi.jp/english/

The local JR trains give nice views of Fuji on the way to Odawara but the Shinkansen route is different and the best views from that train are past Odawara (Shizuoka).

The Odakyu company (which operates the Romance Car, which isn't very romantic) departs from Shinjuku and it saves making a simple transfer.

There are several options - my last trip to Hakone I did via shinkansen. I've done Odakyu trains quite a few times and the 890yen surcharge sometimes isn't worth it - depends on the day/time.

If your primary goal is to see Mount Fuji, you should go to the Five Lakes area, not to Hakone...