<p>Our application is well structured (well we did our best!) and we have split the Model from the View, Now, we need to let some information to our client with a web access. We would like to build something small with IIS and some webform.</p>
<p>Here some information you might think are useful:</p>
<ol>
<li>Our controller have Thread of database queries</li>
<li>Our database is PostGresql</li>
<li>All is build with C#2.0</li>
<li>We used a lot of databinding between our View and Controller in Winform.</li>
<li>Winform will stay for internal purpose, only a small part will be available on the Internet.</li>
</ol>
<p>What are your suggestions for this kind of move?</p>
<h2>Update</h2>
<p>We will host the web in our company server so the database will stay inside the business. No need to duplicate data or any synchronization.</p>

The biggest challenge is going to be synchronizing your database between the local Winforms application and the hosted Webforms application. Once you do that, creating the web app is easy.
If your web application is read only, then you can set up replication. Find a tool that you like. Three that I found through a quick search are:
Slony-I
Mamoth Replicator
Bucardo
If your web application is not read only, then the problem is more difficult. You might want to consider upgrading to .NET 3.0 or 3.5 so you can use WCF. If there is a significant overlap in functionality, you might want to move your data to the web exclusively and expose it through WCF services.