I need your help in finding a product that will measures how far I ride. Would like it so I can move it easily from one bike to another, works in cold weather and costs under $50.00.
Thank you.

There are wireless bike computers, but moving it from bike to bike takes a little bit of time.

There are GPS units that do this. I have a Garmin Edge 200, but it's way above your budget.

If you already have a smart phone, there are very inexpensive apps that do a great job but drain the battery a lot. I've used Cyclemeter on my iPhone and liked it.

There are bike computers (speedo/odo etc) that are designed to work with two or more bikes with different wheel sizes, etc. But a cheap used android phone with some sort of cheap external battery booster may work well. I've tried the GPS on an old Android, and what I have is a separate $12 bike computer for each bike and since they both sit in the shed together, I can quickly add the two totals together. But over the years, that has been less important to me as is the total days riding.

But batteries have challenges in cold weather.

If my Sigma Rox 6.0 is any indication, they're finicky to set up for exact measurements. If the world will not end if you did 8.0 miles or 8.2, then any of those would be fine. Otherwise a basic GPS box or smartphone app would be more accurate.

On second thought, do you really want to know you're going downhill at 8 mph on 2nd gear with a 20mph / gusts to 29mph headwind?

Does the old fashioned mechanical odometer exist anymore?

Get a wired bike computer at Wally World. It will do just fine. They will work in frigid weather, and batteries last a year or so. You can get one for each bike.

I've bought wired computers from dx.com and suntekstore.com and the like. They ship directly from China. They work just fine. The instruction manuals aren't great, but making the devices work is fairly easy anyway.

Thanks everyone for your ideas.

They work fine.

Sunding Electronic Bicycle Computer/Speedometer - Free Shipping - DealExtreme

Cateye

CatEye Wireless CC-MC100W Bike Computer - 2013 Closeout

Here's an old style mechanical odometer that is shown on Amazon. At the price, you could get one for each bike.
Amazon.com : Speedometer Pyramid 26/27 with Resettable Odometer : Odometer For Bicycle : Sports & Outdoors

I can't believe those are still sold!

I was also surprised! Figured I' may find something similar to the type that used to mount on teh front fork and had a "star" wheel that was adjusted close to the spokes, and then you mounted a "pin" on a spoke that turned the star wheel when it came by. I also couldn't believe the price! It seem like the Schwinn odometers cost nearly that back in the late 50's or early 60's! I'm betting the mechanical odometers sold today for that price either aren't real accurate or won't last like the ones I had as a kid.

I have a wired planet bike computer I got for $29 that I do this with. I bought a second handle bar cradle mount and sensor unit from planet bike direct for my second bike ($10). The computer has settings for bike 1 and 2 so you can put in different wheel sizes for each bike if they are not the same. Just have to remember to change setting from 1 to 2 when you switch bikes. Same cradle and sensor on each bike makes it real simple to go back and forth and still accumulate total mileage... This gives you a complete solution with dual sensors and mounts for $40 bucks. Just have to move computer over and switch bike settings.

Batteries all tend to perform worse when they are Cold.

This looks perfect for what I need. Thanks