This all sounds perfectly do-able in a winforms application. Are there any specific questions you wish to ask. However, I'll try and offer some input to what you have added:
"have a bunch (25) of forms that the users will be filling out that will save the data to a database. the forms are some yes/no questions, some fill in, and some drop down choices: pretty basic stuff just collecting data. "
The standard Telerik RadForm, RadTextBox, and other basic form controls will be suitable for this.
"some users will only be viewing these forms and their data; need to have them open automatically in a pdf."
You can use a ReportViewer to view PDF documents in a WinForms application
"in some cases, if the user answers a certain question with a Yes, we need to ask the user (probably with a popup box) if they want to do something, and we have to save that response to a separate database."
This will be much like an ASP.NET app, saving data to your data source based on a click event etc..
Responses would need to be stored somewhere until they can be sent to your standard database, for example saving to a local textfile, xml file or similar.
"would like to have some of the questions appear/disappear based on responses to other questions."
Again, much like ASP.NET, your events can drive which controls are visible
"need to be able to work offline and then update the database when they are connected at a later time"
Hope that helps, but let me know if you need further information