My first choice would be to rent a car and go on my own, but you don't need to make a decision yet. You should not have any trouble renting a car or signing up for a bus trip when you are in Vegas

As time gets closer go to www.weather.com and put Williams, AZ into the search box and then choose the 10 day forecast to see if weather is going to be a problem. You might also put Las Vegas into the search box too. As long as it is not snowing when you plan to go you'll be fine.

If you are not used to driving in snow it's definitely not something I would volunteer to do on vacation if there is a comfortable bus doing the same trip (although I usually avoid bus tours.)

My advice: Rent the car. If you can't make it to the South Rim for any reason, go to see Hoover Dam, Lake Meade, Valley of Fire State Park and Mount Charleston including Red Rocks.
If you want to see a National Park where there is no snow you can go to Death Valley.

Rent the car, book an overnight stay at the Grand Canyon. If weather conditions are bad, cancel both and take a bus tour if that makes you feel safer.

And when I say bad weather, I mean a winter storm has either just occurred or is about to hit that day. There will be snow on the ground at the canyon but generally roads are good to drive unless there's been a recent storm or significant snowfall.

Rent the car, I have done this twice from Vegas and highly recommend it. Be sure to stop at a grocery or the dreaded Walmart for a small Styrofoam cooler for water, good to have. Leave early in the morning, it is breath taking!

We rented a car and drove from Vegas to the Grand Canyon in December. I would definitely recommend that. Most Vegas hotels offer free valet parking so no expense there. The drive was a very quick and beautiful one. We spent the night literally right on the Canyon's edge at Kachina Lodge. (Call, they get cancellations.) I feel this is the best bang for your buck. It is amazing to be able to look out over the Canyon in the quiet and dark of night, a sky full of stars. You will be able to drive the park at your own pace, pulling over for incredible views wherever you please. On the drive back we stopped at the Hoover Dam and Lake Mead. I wasn't in awe of the lake, personally, but did enjoy viewing the Dam from the Pat Tillman Bridge.
We spoke to friends that did the bus tour and one couple who also did the helicopter tour,and all said they wished they had been able to spend more time at the Canyon.

Thanks all for your responses.

Usually we would not hesitate to rent a car as we prefer to explore independently.

However,what concerned us most was the prospect of driving in road conditions that we have never driven on before ie ice/ snow ( remembering it will be February 3) while also driving on "the other side of the road".
Still undecided at this stage.

We are considering the Grand Canyon Tour Company's day trip at $79.90 which returns to the strip around 9.30pm. Has anyone done this tour?

Just because it's February 3rd doesn't mean there will be ice/snow on the road. Unless there's just been a major storm, the roads will be clear. Really the biggest chance of seeing any ice/snow on the road would be the last hour of your trip from Williams to the Grand Canyon. Prior to that, you're travelling through the desert or on a major interstate so little chance of any ice/snow unless there's been a recent storm (in the past day or so).

Hwy 64 from Williams to the Grand Canyon is what you'd want to focus on. By then you'd be on the road for 3.5 - 4 hours already so hopefully you'd be acclimated to driving on the other side.

Honestly, likely your biggest challenge is going to be getting out of Las Vegas while driving on the wrong side of the road. The rest is no big deal .... unless there's been a very recent storm.

I live in a cold climate, far colder than the Grand Canyon but our major roads are all typically clear and dry within a couple days following a storm. Occasionally it will take a bit longer to get them completely clear if it's been a massive storm, but a typical snowfall is cleared off and dealt with pretty quickly.