New Rancher 420 owner

Hello All,
I just purchased my first ATV. Yup, only took me 43 years to get it. I bought A nice, well cared for, 08 Honda Rancher 420. This bike is stock except for the addition of a Warn winch. This will be used primarily for getting into and out of my remote hunting locations. Most riding will be on trails through the woods, tractor trails or fields. I have already replaced all the brakes and rebuilt the master cylinder with the help of some great advice I found researching on this forum. Thanks to all of you who post those threads as they were very helpful. My only job left to do on the bike is to replace the worn tires. Since I’m replacing the tires its a good time to make some upgrades. I’m considering upgrading to a somewhat larger tire with more aggressive tread than the old stock tires. I’m thinking conservative upgrade. The stock tires are currently 24x8x12 front and 24x10x11 rear. I’m considering going to 25 or 26 inch tires to gain a bit of ground clearance. Living in the snow belt of the north east means I’ll be riding in deep snow and lots of mud. I’m not looking to mud bog just make it to camp through the deep rutted trails. I would prefer to not have to make any modifications to the engine or drive train as reliability is most important to me. My question is, Which of these tire sizes would you suggest and what kind of performance loss am I going to experience with the larger tire? I have considered a 2" lift also but am concerned about reliability issues with the changes. Any advice would be greatly appreciated.