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Stock tires:
All Passport trims come equipped with Continental CrossContact LX Sport tires. The difference is only in sizes:
Sport/EX-L come with 245/50-R20 102H
https://www.continentaltire.com/product/crosscontact-lx-sport-24550r20-102h/?
Touring/Elite come with 265/45-R20 108H (108H is unconfirmed at this point but I suspect it's true as it appears to be the cheapest option)
https://www.continentaltire.com/product/crosscontact-lx-sport-26545r20-108h-0/?

Based on TireRack ratings, the Continental CrossContact LX Sport in general are not that bad. They are rated good for dry and wet. They are, however, mediocre on the snow and treadwear is not that great.

I was looking for better performing all season tires with good performance on the snow while trying not to spend money on new rims. I also tried to find alternatives with minimum impact on speedometer.
So, here are what I see to be a good alternatives to stock tires based on these conditions:

Sport/EX-L
Michelin Defender LTX M/S in 255/50-R20 109H - great overall tire, highly praised, good wet and snow traction - this would be my choice.
Also would fit:
BFGoodrich Advantage T/A Sport LT in 245/50-R20 102H - good reviews but not many of them comparing to other
tires
Bridgestone Dueler H/L Alenza Plus in 255/50R20 109V - more expensive because of the higher speed rating (149 mph)

Touring/Elite
Michelin Defender LTX M/S in 265/50-R20 107T - great overall tire, highly praised, good wet and snow traction
Continental TerrainContact A/T in 265/50-R20 107T - a bit more off-road oriented with still good on-road performance
https://www.continentaltire.com/product/terraincontact-26550r20-107t/?

Both above options for Touring/Elite have slightly lower maximum speed (118 mph vs 130 mph for stock tires). But I do not see this being a problem for this vehicle. Both above would be my choice depending on priorities: the first one will likely would give a better gas mileage and the second would give a better off-road performance.
Also would fit:
BFGoodrich Advantage T/A Sport LT in 265/50-R20 111T
Bridgestone Dueler H/L Alenza Plus in 265/50R20 106V

In conclusion: all alternative tires listed above are heavier than stock tires, from about 4 lb (Michelin Defender LTX M/S) and up to 12 lb (Bridgestone Dueler H/L Alenza Plus) per tire.

 

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To give you an idea about speedometer error for these tires.
Continental CrossContact LX Sport 245/50-R20 102H specified with 699 revs per mile.
Continental CrossContact LX Sport 265/45-R20 108H specified with 707 revs per mile.

Lets assume that Passport speedometer is tuned for about 700 revs per mile (I'm leaning toward the first number as it also a standard wheel for Pilot).

Michelin Defender LTX M/S in 255/50-R20 109H specified with 691 revs per mile. So it takes about 1.29% less revs to travel a mile. So when speedometer will read 60, the actual speed would be 60.78.

Michelin Defender LTX M/S in 265/50-R20 107T specified with 683 revs per mile.
Continental TerrainContact A/T in 265/50-R20 107T is also specified with 683 revs per mile.
So it takes about 2.43% less revs to travel a mile. So when speedometer will read 60, the actual speed would be 61.43.

 

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I've got Michelin Defender LTX M/S 225/65-R17 for my wife's '15 CR-V in October as well. She is also very happy with them in the snow and in the rain.

Costco. Paid $687 for 4 tires installed. Considering free tire rotation for the life of tires and replacement based on residual in case of an accident, I do not think I overpaid .

 

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What specific Michelin tires you've had?

So far, there are no any issues with Defender LTX on my wife's CR-V. She drove through the winter and was very pleased with performance. Yes, this winter in Boston was very mild but still we had a fair share of ice and snow. In any case, I got them from Costco and pretty sure they would take care of any issues. So far, this is the third set of tires I've got through them and my experience is very positive.

Premier LTX on another hand (based on the reviews on TireRack) are known to wear off pretty quickly. Comparing the two, the thread is much deeper on Defender LTX.

Nevertheless, there are not many options with good ratings which would fit to replace the stock tires. Do your research and get what's best for you.