I would not solder onto a neodymium magnet as most are low temp magnets and neodymium magnets DO NOT recover from heat, so you will demagnetise your magnet with heat.
neodymium magnets come with a heat rating like N for 80C and M for 120C and most dont go higher than a M rating.
The higher the rating the greater the price, so most cheaper magnets will have a low temp rating.
What i have done is to solder onto a nickle plated steel washer and just stuck that to the magnet, as they are powerful little suckers and it will contact well.
You could use the metal end from a dead AAA battery to solder onto instead of a washer.
If you use a thicker bit of steel on one side of the magnet and a thinner on the other, the magnet will remain stuck to the thicker piece, and the thinner piece will disconnect from the magnet.
Pete.