How to get a (text) selection on a specific page

in the java version, something like this is possible:

PDFViewCtrl.Selection selection = m_pdfViewer.GetSelection(m_pdfViewer.GetCurrentPage);

Is there any way to do the same using winforms?

Yes, the same API exists for WinForms.

http://www.pdftron.com/pdfnet/docs/PDFNet/?topic=html/M_pdftron_PDF_PDFViewCtrl_GetSelection_1.htm

Perhaps you need to update to a newer version of PDFNet.