Windows does not recognize linux file systems such as ext2, ext3, ext4, xfs, or btfs. So no win8 (nor win7 nor win10) would not change your linux drives to read only.
also unless you are using some special newer SSD that I am not aware of where this read-only is happening at the SATA controller level, so whatever linux operating system you are using when it goes to
mount the given filesystems during boot for whatever reason would be doing a read-only mount. Why that might would be is if something dirtied or corrupted the linux type file system and linux recognized that during boot resulting in a disk check and a read-only mount. However to my knowledge there is no linux file system support in win7/8/10 so I think your problem is all within linux and unrelated to windows.
I have 3 ssd's on home pc, win10, centos, rhel. I choose which one at uefi boot time. I don't have any problem like you describe. I mount my win10 ntfs ssd in linux with ntfs-3g all the time with no problems.
It is also recommended to turn off win8 / win10 fast startup so that whenever restarting or shutting down windows it properly flushes its NTFS filesystem and there you will be better off if you mount that ntfs filesystem in linux with ntfs-3g, otherwise you'll likely experience a windows disk check upon every windows boot if it had previously been mounted by linux. There are many online articles describing pro's & con's of
windows fast startup better than i did. In win8 I think it is called